英文维基 | 中文维基 | 日文维基 | 草榴社区
y = k ± b 1 − ( x − h ) 2 a 2 {\displaystyle y=k\pm b{\sqrt {1-{(x-h)^{2} \over a^{2}}}}\,}
m = ∓ b a x − h a 2 − ( x − h ) 2 {\displaystyle m=\mp {b \over a}{x-h \over {\sqrt {a^{2}-(x-h)^{2}}}}\,}
( x 1 , y 1 ) , m 1 ; ( x 2 , y 2 ) , m 2 {\displaystyle (x1,y1),m1;(x2,y2),m2\,}
1 b = ∓ 1 a m x − h a 2 − ( x − h ) 2 {\displaystyle {1 \over b}=\mp {1 \over am}{x-h \over {\sqrt {a^{2}-(x-h)^{2}}}}\,}
b = ∓ a m a 2 − ( x − h ) 2 x − h {\displaystyle b=\mp am{{\sqrt {a^{2}-(x-h)^{2}}} \over x-h}\,}
m 1 a 2 − ( x 1 − h ) 2 x 1 − h {\displaystyle m_{1}{{\sqrt {a^{2}-(x_{1}-h)^{2}}} \over x_{1}-h}\,} = m 2 a 2 − ( x 2 − h ) 2 x 2 − h {\displaystyle =m_{2}{{\sqrt {a^{2}-(x_{2}-h)^{2}}} \over x_{2}-h}\,}
m 1 2 a 2 − ( x 1 − h ) 2 ( x 1 − h ) 2 {\displaystyle m_{1}^{2}{a^{2}-(x_{1}-h)^{2} \over (x_{1}-h)^{2}}\,} = m 2 2 a 2 − ( x 2 − h ) 2 ( x 2 − h ) 2 {\displaystyle =m_{2}^{2}{a^{2}-(x_{2}-h)^{2} \over (x_{2}-h)^{2}}\,}
m 1 2 ( x 2 − h ) 2 [ a 2 − ( x 1 − h ) 2 ] {\displaystyle m_{1}^{2}(x_{2}-h)^{2}[a^{2}-(x_{1}-h)^{2}]\,} = m 2 2 ( x 1 − h ) 2 [ a 2 − ( x 2 − h ) 2 ] {\displaystyle =m_{2}^{2}(x_{1}-h)^{2}[a^{2}-(x_{2}-h)^{2}]\,}
a 2 m 1 2 ( x 2 − h ) 2 − m 1 2 ( x 1 − h ) 2 ( x 2 − h ) 2 {\displaystyle a^{2}m_{1}^{2}(x_{2}-h)^{2}-m_{1}^{2}(x_{1}-h)^{2}(x_{2}-h)^{2}\,} = a 2 m 2 2 ( x 1 − h ) 2 − m 2 2 ( x 1 − h ) 2 ( x 2 − h ) 2 {\displaystyle =a^{2}m_{2}^{2}(x_{1}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}(x_{2}-h)^{2}\,}
a 2 [ m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] {\displaystyle a^{2}[m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]\,} = ( x 1 − h ) 2 ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) {\displaystyle =(x_{1}-h)^{2}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})\,}
a 2 {\displaystyle a^{2}\,} = ( x 1 − h ) 2 ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 {\displaystyle ={(x_{1}-h)^{2}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2}) \over m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}\,}
a {\displaystyle a\,} = ( x 1 − h ) ( x 2 − h ) m 1 2 − m 2 2 m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 {\displaystyle ={(x_{1}-h)(x_{2}-h){\sqrt {m_{1}^{2}-m_{2}^{2}}} \over {\sqrt {m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}}\,}
m 1 = ∓ b a x 1 − h a 2 − ( x 1 − h ) 2 {\displaystyle m_{1}=\mp {b \over a}{x_{1}-h \over {\sqrt {a^{2}-(x_{1}-h)^{2}}}}\,}
b = ∓ m 1 a 4 − a 2 ( x 1 − h ) 2 x 1 − h {\displaystyle b=\mp m_{1}{{\sqrt {a^{4}-a^{2}(x_{1}-h)^{2}}} \over x_{1}-h}\,}
a 4 − a 2 ( x 1 − h ) 2 {\displaystyle a^{4}-a^{2}(x_{1}-h)^{2}\,} とは
= ( ( x 1 − h ) 2 ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ) 2 {\displaystyle =\left({(x_{1}-h)^{2}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2}) \over m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}\right)^{2}\,} − ( ( x 1 − h ) 2 ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ) ( x 1 − h ) 2 {\displaystyle -\left({(x_{1}-h)^{2}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2}) \over m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}\right)(x_{1}-h)^{2}\,}
= ( x 1 − h ) 4 ( x 2 − h ) 4 ( m 1 2 − m 2 2 ) 2 [ m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] 2 {\displaystyle ={(x_{1}-h)^{4}(x_{2}-h)^{4}(m_{1}^{2}-m_{2}^{2})^{2} \over [m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]^{2}}\,} − ( x 1 − h ) 4 ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 {\displaystyle -{(x_{1}-h)^{4}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2}) \over m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}\,}
= ( x 1 − h ) 4 ( x 2 − h ) 4 ( m 1 2 − m 2 2 ) 2 − ( x 1 − h ) 4 ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) [ m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] [ m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] 2 {\displaystyle ={(x_{1}-h)^{4}(x_{2}-h)^{4}(m_{1}^{2}-m_{2}^{2})^{2}-(x_{1}-h)^{4}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})[m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}] \over [m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]^{2}}\,}
= ( x 1 − h ) 4 ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) [ ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) − [ m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] ] [ m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] 2 {\displaystyle ={(x_{1}-h)^{4}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})[(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})-[m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]] \over [m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]^{2}}\,}
= m 2 2 ( x 1 − h ) 4 ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) [ ( x 1 − h ) 2 − ( x 2 − h ) 2 ] [ m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] 2 {\displaystyle ={m_{2}^{2}(x_{1}-h)^{4}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})[(x_{1}-h)^{2}-(x_{2}-h)^{2}] \over [m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]^{2}}\,}
b = ∓ m 1 m 2 2 ( x 1 − h ) 4 ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) [ ( x 1 − h ) 2 − ( x 2 − h ) 2 ] [ m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] 2 x 1 − h {\displaystyle b=\mp m_{1}{\dfrac {\sqrt {\cfrac {m_{2}^{2}(x_{1}-h)^{4}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})[(x_{1}-h)^{2}-(x_{2}-h)^{2}]}{[m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]^{2}}}}{x_{1}-h}}\,}
b = ∓ m 1 2 m 2 2 ( x 1 − h ) 2 ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) [ ( x 1 − h ) 2 − ( x 2 − h ) 2 ] [ m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] 2 {\displaystyle b=\mp {\sqrt {\dfrac {m_{1}^{2}m_{2}^{2}(x_{1}-h)^{2}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})[(x_{1}-h)^{2}-(x_{2}-h)^{2}]}{[m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]^{2}}}}\,}
b = ∓ m 1 m 2 ( x 1 − h ) ( x 2 − h ) ( m 1 2 − m 2 2 ) [ ( x 1 − h ) 2 − ( x 2 − h ) 2 ] m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 {\displaystyle b=\mp {\dfrac {m_{1}m_{2}(x_{1}-h)(x_{2}-h){\sqrt {(m_{1}^{2}-m_{2}^{2})[(x_{1}-h)^{2}-(x_{2}-h)^{2}]}}}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\,}
y 1 − y 2 = ± b [ 1 − ( x 1 − h ) 2 a 2 − 1 − ( x 2 − h ) 2 a 2 ] {\displaystyle y_{1}-y_{2}=\pm b\left[{\sqrt {1-{\cfrac {(x_{1}-h)^{2}}{a^{2}}}}}-{\sqrt {1-{\cfrac {(x_{2}-h)^{2}}{a^{2}}}}}\right]\,}
y 1 − y 2 {\displaystyle y_{1}-y_{2}\,} = ± [ ∓ m 1 m 2 ( x 1 − h ) ( x 2 − h ) ( m 1 2 − m 2 2 ) [ ( x 1 − h ) 2 − ( x 2 − h ) 2 ] m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] {\displaystyle =\pm \left[\mp {\dfrac {m_{1}m_{2}(x_{1}-h)(x_{2}-h){\sqrt {(m_{1}^{2}-m_{2}^{2})[(x_{1}-h)^{2}-(x_{2}-h)^{2}]}}}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]\,} ⋅ [ 1 − ( x 1 − h ) 2 [ ( x 1 − h ) 2 ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] {\displaystyle \cdot \left[{\sqrt {1-{\cfrac {(x_{1}-h)^{2}}{\left[{\cfrac {(x_{1}-h)^{2}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]}}}}\right.\,} − 1 − ( x 2 − h ) 2 [ ( x 1 − h ) 2 ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] ] {\displaystyle \left.-{\sqrt {1-{\cfrac {(x_{2}-h)^{2}}{\left[{\cfrac {(x_{1}-h)^{2}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]}}}}\right]\,}
y 1 − y 2 {\displaystyle y_{1}-y_{2}\,} = − [ m 1 m 2 ( x 1 − h ) ( x 2 − h ) ( m 1 2 − m 2 2 ) [ ( x 1 − h ) 2 − ( x 2 − h ) 2 ] m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] {\displaystyle =-\left[{\dfrac {m_{1}m_{2}(x_{1}-h)(x_{2}-h){\sqrt {(m_{1}^{2}-m_{2}^{2})[(x_{1}-h)^{2}-(x_{2}-h)^{2}]}}}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]\,} ⋅ [ 1 − m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) {\displaystyle \cdot \left[{\sqrt {1-{\cfrac {m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}{(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})}}}}\right.\,} − 1 − m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ( x 1 − h ) 2 ( m 1 2 − m 2 2 ) ] {\displaystyle -\left.{\sqrt {1-{\cfrac {m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}{(x_{1}-h)^{2}(m_{1}^{2}-m_{2}^{2})}}}}\right]\,}
y 1 − y 2 {\displaystyle y_{1}-y_{2}\,} = − [ m 1 m 2 ( x 1 − h ) ( x 2 − h ) ( m 1 2 − m 2 2 ) [ ( x 1 − h ) 2 − ( x 2 − h ) 2 ] m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] {\displaystyle =-\left[{\dfrac {m_{1}m_{2}(x_{1}-h)(x_{2}-h){\sqrt {(m_{1}^{2}-m_{2}^{2})[(x_{1}-h)^{2}-(x_{2}-h)^{2}]}}}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]\,} ⋅ [ [ ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) ] − [ m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] ( x 2 − h ) 2 ( m 1 2 − m 2 2 ) {\displaystyle \cdot \left[{\sqrt {\cfrac {[(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})]-[m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]}{(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})}}}\right.\,} − [ ( x 1 − h ) 2 ( m 1 2 − m 2 2 ) ] − [ m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] ( x 1 − h ) 2 ( m 1 2 − m 2 2 ) ] {\displaystyle -\left.{\sqrt {\cfrac {[(x_{1}-h)^{2}(m_{1}^{2}-m_{2}^{2})]-[m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]}{(x_{1}-h)^{2}(m_{1}^{2}-m_{2}^{2})}}}\right]\,}
y 1 − y 2 {\displaystyle y_{1}-y_{2}\,} = − [ m 1 m 2 ( x 1 − h ) ( x 2 − h ) ( x 1 − h ) 2 − ( x 2 − h ) 2 m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] {\displaystyle =-\left[{\dfrac {m_{1}m_{2}(x_{1}-h)(x_{2}-h){\sqrt {(x_{1}-h)^{2}-(x_{2}-h)^{2}}}}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]\,} ⋅ [ m 2 2 [ ( x 1 − h ) 2 − ( x 2 − h ) 2 ] ( x 2 − h ) 2 − m 1 2 [ ( x 1 − h ) 2 − ( x 2 − h ) 2 ] ( x 1 − h ) 2 ] {\displaystyle \cdot \left[{\sqrt {\cfrac {m_{2}^{2}[(x_{1}-h)^{2}-(x_{2}-h)^{2}]}{(x_{2}-h)^{2}}}}-{\sqrt {\cfrac {m_{1}^{2}[(x_{1}-h)^{2}-(x_{2}-h)^{2}]}{(x_{1}-h)^{2}}}}\right]\,}
y 1 − y 2 {\displaystyle y_{1}-y_{2}\,} = − ( x 1 − h ) 2 − ( x 2 − h ) 2 {\displaystyle =-{\sqrt {(x_{1}-h)^{2}-(x_{2}-h)^{2}}}\,} ⋅ [ m 1 m 2 ( x 1 − h ) ( x 2 − h ) m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] {\displaystyle \cdot \left[{\dfrac {m_{1}m_{2}(x_{1}-h)(x_{2}-h)}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]\,} ⋅ [ m 2 2 ( x 2 − h ) 2 − m 1 2 ( x 1 − h ) 2 ] {\displaystyle \cdot \left[{\sqrt {\cfrac {m_{2}^{2}}{(x_{2}-h)^{2}}}}-{\sqrt {\cfrac {m_{1}^{2}}{(x_{1}-h)^{2}}}}\right]\,}
y 1 − y 2 {\displaystyle y_{1}-y_{2}\,} = − ( x 1 − h ) 2 − ( x 2 − h ) 2 {\displaystyle =-{\sqrt {(x_{1}-h)^{2}-(x_{2}-h)^{2}}}\,} ⋅ [ m 1 m 2 ( x 1 − h ) ( x 2 − h ) m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] {\displaystyle \cdot \left[{\dfrac {m_{1}m_{2}(x_{1}-h)(x_{2}-h)}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]\,} ⋅ [ m 2 x 2 − h − m 1 x 1 − h ] {\displaystyle \cdot \left[{\dfrac {m_{2}}{x_{2}-h}}-{\dfrac {m_{1}}{x_{1}-h}}\right]\,}
y 1 − y 2 {\displaystyle y_{1}-y_{2}\,} = − ( x 1 − h ) 2 − ( x 2 − h ) 2 {\displaystyle =-{\sqrt {(x_{1}-h)^{2}-(x_{2}-h)^{2}}}\,} ⋅ [ m 1 m 2 ( x 1 − h ) ( x 2 − h ) m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] {\displaystyle \cdot \left[{\dfrac {m_{1}m_{2}(x_{1}-h)(x_{2}-h)}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]\,} ⋅ [ m 2 ( x 1 − h ) − m 1 ( x 2 − h ) ( x 1 − h ) ( x 2 − h ) ] {\displaystyle \cdot \left[{\dfrac {m_{2}(x_{1}-h)-m_{1}(x_{2}-h)}{(x_{1}-h)(x_{2}-h)}}\right]\,}
y 1 − y 2 {\displaystyle y_{1}-y_{2}\,} = ( x 1 − h ) 2 − ( x 2 − h ) 2 {\displaystyle ={\sqrt {(x_{1}-h)^{2}-(x_{2}-h)^{2}}}\,} ⋅ [ m 1 m 2 m 1 2 ( x 2 − h ) 2 − m 2 2 ( x 1 − h ) 2 ] {\displaystyle \cdot \left[{\dfrac {m_{1}m_{2}}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]\,} ⋅ [ m 1 ( x 2 − h ) − m 2 ( x 1 − h ) ] {\displaystyle \cdot [m_{1}(x_{2}-h)-m_{2}(x_{1}-h)]\,}
y 1 − y 2 {\displaystyle y_{1}-y_{2}\,} = ( x 1 − h ) 2 − ( x 2 − h ) 2 {\displaystyle ={\sqrt {(x_{1}-h)^{2}-(x_{2}-h)^{2}}}\,} ⋅ [ m 1 m 2 m 1 ( x 2 − h ) + m 2 ( x 1 − h ) ] {\displaystyle \cdot \left[{\dfrac {m_{1}m_{2}}{m_{1}(x_{2}-h)+m_{2}(x_{1}-h)}}\right]\,}
y 1 − y 2 m 1 m 2 {\displaystyle {\dfrac {y_{1}-y_{2}}{m_{1}m_{2}}}\,} = ( x 1 − h ) 2 − ( x 2 − h ) 2 m 1 ( x 2 − h ) + m 2 ( x 1 − h ) {\displaystyle ={\dfrac {\sqrt {(x_{1}-h)^{2}-(x_{2}-h)^{2}}}{m_{1}(x_{2}-h)+m_{2}(x_{1}-h)}}\,}
( y 1 − y 2 ) 2 m 1 2 m 2 2 {\displaystyle {\dfrac {(y_{1}-y_{2})^{2}}{m_{1}^{2}m_{2}^{2}}}\,} = ( x 1 − h ) 2 − ( x 2 − h ) 2 m 1 2 ( x 2 − h ) 2 + 2 m 1 m 2 ( x 1 − h ) ( x 2 − h ) + m 2 2 ( x 1 − h ) 2 {\displaystyle ={\dfrac {(x_{1}-h)^{2}-(x_{2}-h)^{2}}{m_{1}^{2}(x_{2}-h)^{2}+2m_{1}m_{2}(x_{1}-h)(x_{2}-h)+m_{2}^{2}(x_{1}-h)^{2}}}\,}
( y 1 − y 2 ) 2 m 1 2 m 2 2 {\displaystyle {\dfrac {(y_{1}-y_{2})^{2}}{m_{1}^{2}m_{2}^{2}}}\,} = x 1 2 − x 2 2 − 2 h ( x 1 − x 2 ) m 1 2 ( x 2 2 − 2 h x 2 + h 2 ) + 2 m 1 m 2 [ x 1 x 2 − h ( x 1 + x 2 ) + h 2 ] + m 2 2 ( x 1 2 − 2 h x 1 + h 2 ) {\displaystyle ={\dfrac {x_{1}^{2}-x_{2}^{2}-2h(x_{1}-x_{2})}{m_{1}^{2}(x_{2}^{2}-2hx_{2}+h^{2})+2m_{1}m_{2}[x_{1}x_{2}-h(x_{1}+x_{2})+h^{2}]+m_{2}^{2}(x_{1}^{2}-2hx_{1}+h^{2})}}\,}
m 1 2 m 2 2 ( y 1 − y 2 ) 2 {\displaystyle {\dfrac {m_{1}^{2}m_{2}^{2}}{(y_{1}-y_{2})^{2}}}\,} = ( m 1 2 + 2 m 1 m 2 + m 2 2 ) h 2 + [ − 2 m 1 2 x 2 − 2 m 1 m 2 ( x 1 + x 2 ) − 2 m 2 2 x 1 ] h + ( m 1 2 x 2 2 + 2 m 1 m 2 x 1 x 2 + m 2 2 x 1 2 ) − 2 ( x 1 − x 2 ) h + x 1 2 − x 2 2 {\displaystyle ={\dfrac {(m_{1}^{2}+2m_{1}m_{2}+m_{2}^{2})h^{2}+[-2m_{1}^{2}x_{2}-2m_{1}m_{2}(x_{1}+x_{2})-2m_{2}^{2}x_{1}]h+(m_{1}^{2}x_{2}^{2}+2m_{1}m_{2}x_{1}x_{2}+m_{2}^{2}x_{1}^{2})}{-2(x_{1}-x_{2})h+x_{1}^{2}-x_{2}^{2}}}\,}
m 1 2 m 2 2 ( y 1 − y 2 ) 2 {\displaystyle {\dfrac {m_{1}^{2}m_{2}^{2}}{(y_{1}-y_{2})^{2}}}\,} = ( m 1 + m 2 ) 2 h 2 − [ 2 m 1 2 x 2 + 2 m 1 m 2 ( x 1 + x 2 ) + 2 m 2 2 x 1 ] h + ( m 1 x 2 + m 2 x 1 ) 2 − 2 ( x 1 − x 2 ) h + x 1 2 − x 2 2 {\displaystyle ={\dfrac {(m_{1}+m_{2})^{2}h^{2}-[2m_{1}^{2}x_{2}+2m_{1}m_{2}(x_{1}+x_{2})+2m_{2}^{2}x_{1}]h+(m_{1}x_{2}+m_{2}x_{1})^{2}}{-2(x_{1}-x_{2})h+x_{1}^{2}-x_{2}^{2}}}\,}
( m 1 2 m 2 2 ) [ − 2 ( x 1 − x 2 ) h + x 1 2 − x 2 2 ] ( y 1 − y 2 ) 2 {\displaystyle {\dfrac {(m_{1}^{2}m_{2}^{2})[-2(x_{1}-x_{2})h+x_{1}^{2}-x_{2}^{2}]}{(y_{1}-y_{2})^{2}}}\,} = ( m 1 + m 2 ) 2 h 2 {\displaystyle =(m_{1}+m_{2})^{2}h^{2}\,} − [ 2 m 1 2 x 2 + 2 m 1 m 2 ( x 1 + x 2 ) + 2 m 2 2 x 1 ] h {\displaystyle -[2m_{1}^{2}x_{2}+2m_{1}m_{2}(x_{1}+x_{2})+2m_{2}^{2}x_{1}]h\,} + ( m 1 x 2 + m 2 x 1 ) 2 {\displaystyle +(m_{1}x_{2}+m_{2}x_{1})^{2}\,}
0 {\displaystyle 0\,} = ( m 1 + m 2 ) 2 h 2 {\displaystyle =(m_{1}+m_{2})^{2}h^{2}\,} − [ 2 ( m 1 + m 2 ) ( m 1 x 2 + m 2 x 1 ) ] h {\displaystyle -[2(m_{1}+m_{2})(m_{1}x_{2}+m_{2}x_{1})]h\,} + ( m 1 x 2 + m 2 x 1 ) 2 {\displaystyle +(m_{1}x_{2}+m_{2}x_{1})^{2}\,} − − 2 m 1 2 m 2 2 ( x 1 − x 2 ) h + m 1 2 m 2 2 ( x 1 2 − x 2 2 ) ( y 1 − y 2 ) 2 {\displaystyle -{\dfrac {-2m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})h+m_{1}^{2}m_{2}^{2}(x_{1}^{2}-x_{2}^{2})}{(y_{1}-y_{2})^{2}}}\,}
0 {\displaystyle 0\,} = [ ( m 1 + m 2 ) 2 ] h 2 {\displaystyle =\left[(m_{1}+m_{2})^{2}\right]h^{2}\,} + [ − 2 ( y 1 − y 2 ) 2 ( m 1 + m 2 ) ( m 1 x 2 + m 2 x 1 ) − m 1 2 m 2 2 ( x 1 − x 2 ) ( y 1 − y 2 ) 2 ] h {\displaystyle +\left[-2{\dfrac {(y_{1}-y_{2})^{2}(m_{1}+m_{2})(m_{1}x_{2}+m_{2}x_{1})-m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})}{(y_{1}-y_{2})^{2}}}\right]h\,} + [ ( y 1 − y 2 ) 2 ( m 1 x 2 + m 2 x 1 ) 2 + m 1 2 m 2 2 ( x 1 2 − x 2 2 ) ( y 1 − y 2 ) 2 ] {\displaystyle +\left[{\dfrac {(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})^{2}+m_{1}^{2}m_{2}^{2}(x_{1}^{2}-x_{2}^{2})}{(y_{1}-y_{2})^{2}}}\right]\,}
h {\displaystyle h\,} = 1 2 [ ( m 1 + m 2 ) 2 ] {\displaystyle ={\dfrac {1}{2\left[(m_{1}+m_{2})^{2}\right]}}\,} [ − [ − 2 ( y 1 − y 2 ) 2 ( m 1 + m 2 ) ( m 1 x 2 + m 2 x 1 ) − m 1 2 m 2 2 ( x 1 − x 2 ) ( y 1 − y 2 ) 2 ] {\displaystyle \left[-\left[-2{\dfrac {(y_{1}-y_{2})^{2}(m_{1}+m_{2})(m_{1}x_{2}+m_{2}x_{1})-m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})}{(y_{1}-y_{2})^{2}}}\right]\right.\,} ± [ − 2 ( y 1 − y 2 ) 2 ( m 1 + m 2 ) ( m 1 x 2 + m 2 x 1 ) − m 1 2 m 2 2 ( x 1 − x 2 ) ( y 1 − y 2 ) 2 ] 2 − 4 [ ( m 1 + m 2 ) 2 ] [ ( y 1 − y 2 ) 2 ( m 1 x 2 + m 2 x 1 ) 2 + m 1 2 m 2 2 ( x 1 2 − x 2 2 ) ( y 1 − y 2 ) 2 ] ] {\displaystyle \pm \left.{\sqrt {\left[-2{\cfrac {(y_{1}-y_{2})^{2}(m_{1}+m_{2})(m_{1}x_{2}+m_{2}x_{1})-m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})}{(y_{1}-y_{2})^{2}}}\right]^{2}-4\left[(m_{1}+m_{2})^{2}\right]\left[{\cfrac {(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})^{2}+m_{1}^{2}m_{2}^{2}(x_{1}^{2}-x_{2}^{2})}{(y_{1}-y_{2})^{2}}}\right]}}\right]\,}
h {\displaystyle h\,} = 1 m 1 + m 2 {\displaystyle ={\dfrac {1}{m_{1}+m_{2}}}\,} [ ( y 1 − y 2 ) 2 ( m 1 x 2 + m 2 x 1 ) − m 1 2 m 2 2 ( x 1 − x 2 ) ( y 1 − y 2 ) 2 {\displaystyle \left[{\dfrac {(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})-m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})}{(y_{1}-y_{2})^{2}}}\right.\,} ± [ − ( y 1 − y 2 ) 2 ( m 1 x 2 + m 2 x 1 ) − m 1 2 m 2 2 ( x 1 − x 2 ) ( y 1 − y 2 ) 2 ] 2 − [ ( y 1 − y 2 ) 2 ( m 1 x 2 + m 2 x 1 ) 2 + m 1 2 m 2 2 ( x 1 2 − x 2 2 ) ( y 1 − y 2 ) 2 ] ] {\displaystyle \pm \left.{\sqrt {\left[-{\cfrac {(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})-m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})}{(y_{1}-y_{2})^{2}}}\right]^{2}-\left[{\cfrac {(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})^{2}+m_{1}^{2}m_{2}^{2}(x_{1}^{2}-x_{2}^{2})}{(y_{1}-y_{2})^{2}}}\right]}}\right]\,}
h {\displaystyle h\,} = 1 m 1 + m 2 {\displaystyle ={\dfrac {1}{m_{1}+m_{2}}}\,} [ ( y 1 − y 2 ) 2 ( m 1 x 2 + m 2 x 1 ) − m 1 2 m 2 2 ( x 1 − x 2 ) ( y 1 − y 2 ) 2 {\displaystyle \left[{\dfrac {(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})-m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})}{(y_{1}-y_{2})^{2}}}\right.\,} ± ( y 1 − y 2 ) 4 ( m 1 x 2 + m 2 x 1 ) 2 − 2 m 1 2 m 2 2 ( y 1 − y 2 ) 2 ( m 1 x 2 + m 2 x 1 ) ( x 1 − x 2 ) + m 1 4 m 2 4 ( x 1 − x 2 ) 4 ( y 1 − y 2 ) 4 − ( y 1 − y 2 ) 4 ( m 1 x 2 + m 2 x 1 ) 2 + ( y 1 − y 2 ) 2 m 1 2 m 2 2 ( x 1 2 − x 2 2 ) ( y 1 − y 2 ) 4 ] {\displaystyle \pm \left.{\sqrt {{\cfrac {(y_{1}-y_{2})^{4}(m_{1}x_{2}+m_{2}x_{1})^{2}-2m_{1}^{2}m_{2}^{2}(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})(x_{1}-x_{2})+m_{1}^{4}m_{2}^{4}(x_{1}-x_{2})^{4}}{(y_{1}-y_{2})^{4}}}-{\cfrac {(y_{1}-y_{2})^{4}(m_{1}x_{2}+m_{2}x_{1})^{2}+(y_{1}-y_{2})^{2}m_{1}^{2}m_{2}^{2}(x_{1}^{2}-x_{2}^{2})}{(y_{1}-y_{2})^{4}}}}}\right]\,}
h {\displaystyle h\,} = 1 ( m 1 + m 2 ) ( y 1 − y 2 ) 2 {\displaystyle ={\dfrac {1}{(m_{1}+m_{2})(y_{1}-y_{2})^{2}}}\,} [ ( y 1 − y 2 ) 2 ( m 1 x 2 + m 2 x 1 ) − m 1 2 m 2 2 ( x 1 − x 2 ) {\displaystyle \left[(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})-m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})\right.\,} ± m 1 m 2 [ − 2 ( y 1 − y 2 ) 2 ( m 1 x 2 + m 2 x 1 ) ( x 1 − x 2 ) + m 1 2 m 2 2 ( x 1 − x 2 ) 4 ] − [ ( y 1 − y 2 ) 2 ( x 1 2 − x 2 2 ) ] ] {\displaystyle \pm \left.m_{1}m_{2}{\sqrt {[-2(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})(x_{1}-x_{2})+m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})^{4}]-[(y_{1}-y_{2})^{2}(x_{1}^{2}-x_{2}^{2})]}}\right]\,}
h {\displaystyle h\,} = 1 ( m 1 + m 2 ) ( y 1 − y 2 ) 2 {\displaystyle ={\dfrac {1}{(m_{1}+m_{2})(y_{1}-y_{2})^{2}}}\,} [ ( y 1 − y 2 ) 2 ( m 1 x 2 + m 2 x 1 ) − m 1 2 m 2 2 ( x 1 − x 2 ) {\displaystyle \left[(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})-m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})\right.\,} ± m 1 m 2 m 1 2 m 2 2 ( x 1 − x 2 ) 4 − ( y 1 − y 2 ) 2 [ 2 ( m 1 x 2 + m 2 x 1 ) ( x 1 − x 2 ) + ( x 1 2 − x 2 2 ) ] ] {\displaystyle \pm \left.m_{1}m_{2}{\sqrt {m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})^{4}-(y_{1}-y_{2})^{2}[2(m_{1}x_{2}+m_{2}x_{1})(x_{1}-x_{2})+(x_{1}^{2}-x_{2}^{2})]}}\right]\,}
![{\displaystyle m_{1}^{2}(x_{2}-h)^{2}[a^{2}-(x_{1}-h)^{2}]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/981644133e4889ccbef843434d89cde99ff9d990)
![{\displaystyle =m_{2}^{2}(x_{1}-h)^{2}[a^{2}-(x_{2}-h)^{2}]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d3fbda04a238ad95ed9e159108a20e1c42e8120a)
![{\displaystyle a^{2}[m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/11c6157cc0f9c7f8e94d267a8e412db234b6278a)
とは
![{\displaystyle ={(x_{1}-h)^{4}(x_{2}-h)^{4}(m_{1}^{2}-m_{2}^{2})^{2} \over [m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]^{2}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8a642970e0d8d1be69654349573616bced27389e)
![{\displaystyle ={(x_{1}-h)^{4}(x_{2}-h)^{4}(m_{1}^{2}-m_{2}^{2})^{2}-(x_{1}-h)^{4}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})[m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}] \over [m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]^{2}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c87b18c5165cd86534ce9ff73606c503bb6a3b90)
![{\displaystyle ={(x_{1}-h)^{4}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})[(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})-[m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]] \over [m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]^{2}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f83a13a046bb49e14bc934ad7f219a96fca9a016)
![{\displaystyle ={m_{2}^{2}(x_{1}-h)^{4}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})[(x_{1}-h)^{2}-(x_{2}-h)^{2}] \over [m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]^{2}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1e665490fa7de7d3c21a92be9b8e2a13e69ab636)
![{\displaystyle b=\mp m_{1}{\dfrac {\sqrt {\cfrac {m_{2}^{2}(x_{1}-h)^{4}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})[(x_{1}-h)^{2}-(x_{2}-h)^{2}]}{[m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]^{2}}}}{x_{1}-h}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2511baa6d90f58d20e4e787406ef7017275a03d0)
![{\displaystyle b=\mp {\sqrt {\dfrac {m_{1}^{2}m_{2}^{2}(x_{1}-h)^{2}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})[(x_{1}-h)^{2}-(x_{2}-h)^{2}]}{[m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]^{2}}}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1bcf3f6230edb0ccf130398c937f4e729fee517e)
![{\displaystyle b=\mp {\dfrac {m_{1}m_{2}(x_{1}-h)(x_{2}-h){\sqrt {(m_{1}^{2}-m_{2}^{2})[(x_{1}-h)^{2}-(x_{2}-h)^{2}]}}}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e8d991fbff6ad4f2c5b645842954b354d56a90e1)
![{\displaystyle y_{1}-y_{2}=\pm b\left[{\sqrt {1-{\cfrac {(x_{1}-h)^{2}}{a^{2}}}}}-{\sqrt {1-{\cfrac {(x_{2}-h)^{2}}{a^{2}}}}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4671a051871b6fc6ed72a6b1067f296f46427a73)
![{\displaystyle =\pm \left[\mp {\dfrac {m_{1}m_{2}(x_{1}-h)(x_{2}-h){\sqrt {(m_{1}^{2}-m_{2}^{2})[(x_{1}-h)^{2}-(x_{2}-h)^{2}]}}}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7556c911dfbdf5f32b4e66c52e600229afc459d3)
![{\displaystyle \cdot \left[{\sqrt {1-{\cfrac {(x_{1}-h)^{2}}{\left[{\cfrac {(x_{1}-h)^{2}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]}}}}\right.\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/32cbcde2e1daabd9cc46ded2eff7bc795d352ad0)
![{\displaystyle \left.-{\sqrt {1-{\cfrac {(x_{2}-h)^{2}}{\left[{\cfrac {(x_{1}-h)^{2}(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]}}}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ab9edb2bedec7629bbd5c001290372415d2dcc76)
![{\displaystyle =-\left[{\dfrac {m_{1}m_{2}(x_{1}-h)(x_{2}-h){\sqrt {(m_{1}^{2}-m_{2}^{2})[(x_{1}-h)^{2}-(x_{2}-h)^{2}]}}}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4343fc75f4f4347ba191bdded1cdeafe959b0234)
![{\displaystyle -\left.{\sqrt {1-{\cfrac {m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}{(x_{1}-h)^{2}(m_{1}^{2}-m_{2}^{2})}}}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0242a866bb2d58403fe12f4d242ce53221839751)
![{\displaystyle \cdot \left[{\sqrt {\cfrac {[(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})]-[m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]}{(x_{2}-h)^{2}(m_{1}^{2}-m_{2}^{2})}}}\right.\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b08285ad3f0a237cdebe39b456bf4fa902d87756)
![{\displaystyle -\left.{\sqrt {\cfrac {[(x_{1}-h)^{2}(m_{1}^{2}-m_{2}^{2})]-[m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}]}{(x_{1}-h)^{2}(m_{1}^{2}-m_{2}^{2})}}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1a3f45d1fce04ffe54a94bdd0644c87851c0ded4)
![{\displaystyle =-\left[{\dfrac {m_{1}m_{2}(x_{1}-h)(x_{2}-h){\sqrt {(x_{1}-h)^{2}-(x_{2}-h)^{2}}}}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/09250b1057981514a11747b12e6a97c2a631847d)
![{\displaystyle \cdot \left[{\sqrt {\cfrac {m_{2}^{2}[(x_{1}-h)^{2}-(x_{2}-h)^{2}]}{(x_{2}-h)^{2}}}}-{\sqrt {\cfrac {m_{1}^{2}[(x_{1}-h)^{2}-(x_{2}-h)^{2}]}{(x_{1}-h)^{2}}}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc93b489c75cc07b3645fd668d90d68a175698f)
![{\displaystyle \cdot \left[{\dfrac {m_{1}m_{2}(x_{1}-h)(x_{2}-h)}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/653c8cbd8f284ef938e8e80bab905583c79056b5)
![{\displaystyle \cdot \left[{\sqrt {\cfrac {m_{2}^{2}}{(x_{2}-h)^{2}}}}-{\sqrt {\cfrac {m_{1}^{2}}{(x_{1}-h)^{2}}}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7452d0c440be0b7e1433dbf408a22df8fac374c3)
![{\displaystyle \cdot \left[{\dfrac {m_{2}}{x_{2}-h}}-{\dfrac {m_{1}}{x_{1}-h}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b1a832d1b268ea1c56f619bd5e976290027b5407)
![{\displaystyle \cdot \left[{\dfrac {m_{2}(x_{1}-h)-m_{1}(x_{2}-h)}{(x_{1}-h)(x_{2}-h)}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/27ed98edacc05c5c0cb7627f975cc092d4b6eecf)
![{\displaystyle \cdot \left[{\dfrac {m_{1}m_{2}}{m_{1}^{2}(x_{2}-h)^{2}-m_{2}^{2}(x_{1}-h)^{2}}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5a9bcfdea14adf8937757f2bf960fb34f6a5c4e3)
![{\displaystyle \cdot [m_{1}(x_{2}-h)-m_{2}(x_{1}-h)]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6c36f525c18ca0f27d041baf5aa78ed5911eb5e1)
![{\displaystyle \cdot \left[{\dfrac {m_{1}m_{2}}{m_{1}(x_{2}-h)+m_{2}(x_{1}-h)}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0cce8dc2a016fa94593d8d751409d8a0473cb4ac)
![{\displaystyle ={\dfrac {x_{1}^{2}-x_{2}^{2}-2h(x_{1}-x_{2})}{m_{1}^{2}(x_{2}^{2}-2hx_{2}+h^{2})+2m_{1}m_{2}[x_{1}x_{2}-h(x_{1}+x_{2})+h^{2}]+m_{2}^{2}(x_{1}^{2}-2hx_{1}+h^{2})}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b9a7a811daf2b00d4d720d4e117c0f5294614365)
![{\displaystyle ={\dfrac {(m_{1}^{2}+2m_{1}m_{2}+m_{2}^{2})h^{2}+[-2m_{1}^{2}x_{2}-2m_{1}m_{2}(x_{1}+x_{2})-2m_{2}^{2}x_{1}]h+(m_{1}^{2}x_{2}^{2}+2m_{1}m_{2}x_{1}x_{2}+m_{2}^{2}x_{1}^{2})}{-2(x_{1}-x_{2})h+x_{1}^{2}-x_{2}^{2}}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b963c306c1ea6b5d32d862cfc9130284bf1a03af)
![{\displaystyle ={\dfrac {(m_{1}+m_{2})^{2}h^{2}-[2m_{1}^{2}x_{2}+2m_{1}m_{2}(x_{1}+x_{2})+2m_{2}^{2}x_{1}]h+(m_{1}x_{2}+m_{2}x_{1})^{2}}{-2(x_{1}-x_{2})h+x_{1}^{2}-x_{2}^{2}}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6585bb5cd5fbc135d7bdc86738563174c7072649)
![{\displaystyle {\dfrac {(m_{1}^{2}m_{2}^{2})[-2(x_{1}-x_{2})h+x_{1}^{2}-x_{2}^{2}]}{(y_{1}-y_{2})^{2}}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dea4212e246bc636c32f0b12e9252079240f1369)
![{\displaystyle -[2m_{1}^{2}x_{2}+2m_{1}m_{2}(x_{1}+x_{2})+2m_{2}^{2}x_{1}]h\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b202f95a17e01ce075bb127bcf80bb8ad5806502)
![{\displaystyle -[2(m_{1}+m_{2})(m_{1}x_{2}+m_{2}x_{1})]h\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/14e74c776c3077c8f64d1482b6712e384dbbb703)
![{\displaystyle =\left[(m_{1}+m_{2})^{2}\right]h^{2}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d9e6f25a73f592a21e33b9eef375a473bae53de)
![{\displaystyle +\left[-2{\dfrac {(y_{1}-y_{2})^{2}(m_{1}+m_{2})(m_{1}x_{2}+m_{2}x_{1})-m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})}{(y_{1}-y_{2})^{2}}}\right]h\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ab4b07800e93cddc486355248cb3ef7ec4ba8ad3)
![{\displaystyle +\left[{\dfrac {(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})^{2}+m_{1}^{2}m_{2}^{2}(x_{1}^{2}-x_{2}^{2})}{(y_{1}-y_{2})^{2}}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/df225d3239b61bdbbbd66d6524e408fb3f128cf3)
![{\displaystyle ={\dfrac {1}{2\left[(m_{1}+m_{2})^{2}\right]}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b6e86740187a91c97e8c1f4c8753212e3f87789b)
![{\displaystyle \left[-\left[-2{\dfrac {(y_{1}-y_{2})^{2}(m_{1}+m_{2})(m_{1}x_{2}+m_{2}x_{1})-m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})}{(y_{1}-y_{2})^{2}}}\right]\right.\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fb226fa78216df205bcc2fc9b9013b531bd9f5cc)
![{\displaystyle \pm \left.{\sqrt {\left[-2{\cfrac {(y_{1}-y_{2})^{2}(m_{1}+m_{2})(m_{1}x_{2}+m_{2}x_{1})-m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})}{(y_{1}-y_{2})^{2}}}\right]^{2}-4\left[(m_{1}+m_{2})^{2}\right]\left[{\cfrac {(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})^{2}+m_{1}^{2}m_{2}^{2}(x_{1}^{2}-x_{2}^{2})}{(y_{1}-y_{2})^{2}}}\right]}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/97976604fdd33f1662681d895d1eb27a8159e085)
![{\displaystyle \pm \left.{\sqrt {\left[-{\cfrac {(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})-m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})}{(y_{1}-y_{2})^{2}}}\right]^{2}-\left[{\cfrac {(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})^{2}+m_{1}^{2}m_{2}^{2}(x_{1}^{2}-x_{2}^{2})}{(y_{1}-y_{2})^{2}}}\right]}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/10cca073eac23a64b41b8e00480d9bae0d99ea71)
![{\displaystyle \pm \left.{\sqrt {{\cfrac {(y_{1}-y_{2})^{4}(m_{1}x_{2}+m_{2}x_{1})^{2}-2m_{1}^{2}m_{2}^{2}(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})(x_{1}-x_{2})+m_{1}^{4}m_{2}^{4}(x_{1}-x_{2})^{4}}{(y_{1}-y_{2})^{4}}}-{\cfrac {(y_{1}-y_{2})^{4}(m_{1}x_{2}+m_{2}x_{1})^{2}+(y_{1}-y_{2})^{2}m_{1}^{2}m_{2}^{2}(x_{1}^{2}-x_{2}^{2})}{(y_{1}-y_{2})^{4}}}}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f68d081408116f19612423316b0ee05a57f09b89)
![{\displaystyle \pm \left.m_{1}m_{2}{\sqrt {[-2(y_{1}-y_{2})^{2}(m_{1}x_{2}+m_{2}x_{1})(x_{1}-x_{2})+m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})^{4}]-[(y_{1}-y_{2})^{2}(x_{1}^{2}-x_{2}^{2})]}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/13d1734da6cb3af73f49a1c320072963fd424056)
![{\displaystyle \pm \left.m_{1}m_{2}{\sqrt {m_{1}^{2}m_{2}^{2}(x_{1}-x_{2})^{4}-(y_{1}-y_{2})^{2}[2(m_{1}x_{2}+m_{2}x_{1})(x_{1}-x_{2})+(x_{1}^{2}-x_{2}^{2})]}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b50cdaaf2ae6d9daa062a14df77078f3613b110d)
