Question

已知曲线C上任意一点M到点F(1,0)的距离比M到y轴距离大1,求c得方程.过点F的...

Answer 1

令:M(x,y)

|MF|-|y|=1

=>(|y|+1)^2=|MF|^2

=>(1)y=1/2x^2-x(2)y=x-1/2x^2

令:y=kx-k

(1)x^2-2(k+1)x+2k=0

=>x1+x2=2k+2,x1x2=2k

=>|AB|^2=(1+k^2)(x1-x2)^2

=>k=±√3

=>y=±√3x+±√3

(2)同理：

=>y=±√3x+±√3