垂足(x,y),c>0,右焦點(c,0),設a>b,則c=√(a^2-b^2) 設動切線垂線:y=kx+m 橢圓x^2/a^2+y^2/b^2=1 b^2*x^2+a^2*y^2=(ab)^2 b^2*x^2+a^2*(kx+m)^2=(ab)^2 (b^2+a^2*k^2)*x^2+2a^2*kmx+(am)^2-(ab)^2=0 y=kx+m與橢圓（x^2/a^2+y^2/b^2=1）相切，上方程的判別式△=0，即 (2a^2*km)^2-4(b^2+a^2*k^2)*[(am)^2-(ab)^2]=0 m^2=b^2+(ak)^2 m=±√[b^2+(ak)^2] y=kx±√[b^2+(ak)^2] y-kx=±√[b^2+(ak)^2] y^2+x^2*k^2-2xyk=b^2+a^2*k^2 (x^2-a^2)k^2-2xyk+y^2-b^2=0 b^2*x^2+a^2*y^2=(ab)^2 動切線k1=[xy±√(x^2*b^2+a^2*y^2-a^2*b^2)]/(x^2-a^2)=xy/(x^2-a^2) 動切線垂線k2=y/(x-c) k2*k1=-1 [y/(x-c)]*[xy/(x^2-a^2)]=-1 x^3+(a^2-x^2)c+xy^2-xa^2=0 x^3+(a^2-x^2)*√(a^2-b^2)+xy^2-xa^2=0 方法正確，請檢驗一下。
垂足(x,y),c>0,右焦點(c,0),設a>b,則c=√(a^2-b^2) 設動切線垂線:y=kx+m 橢圓x^2/a^2+y^2/b^2=1 b^2*x^2+a^2*y^2=(ab)^2 b^2*x^2+a^2*(kx+m)^2=(ab)^2 (b^2+a^2*k^2)*x^2+2a^2*kmx+(am)^2-(ab)^2=0 y=kx+m與橢圓（x^2/a^2+y^2/b^2=1）相切，上方程的判別式△=0，即 (2a^2*km)^2-4(b^2+a^2*k^2)*[(am)^2-(ab)^2]=0 m^2=b^2+(ak)^2 m=±√[b^2+(ak)^2] y=kx±√[b^2+(ak)^2] y-kx=±√[b^2+(ak)^2] y^2+x^2*k^2-2xyk=b^2+a^2*k^2 (x^2-a^2)k^2-2xyk+y^2-b^2=0 b^2*x^2+a^2*y^2=(ab)^2 動切線k1=[xy±√(x^2*b^2+a^2*y^2-a^2*b^2)]/(x^2-a^2)=xy/(x^2-a^2) 動切線垂線k2=y/(x-c) k2*k1=-1 [y/(x-c)]*[xy/(x^2-a^2)]=-1 x^3+(a^2-x^2)c+xy^2-xa^2=0 x^3+(a^2-x^2)*√(a^2-b^2)+xy^2-xa^2=0 方法正確，請檢驗一下。