Question

直线X-Y-1=0截抛物线Y^2=8X,所截得的弦中点坐标是

Answer 1

{X - Y - 1 == 0, Y^2 == 8 X}

解得

X -> 5 - 2 Sqrt[6], Y -> 2 (2 - Sqrt[6]),

X -> 5 + 2 Sqrt[6], Y -> 2 (2 + Sqrt[6]).

所以中点坐标

X -> 5 , Y -> 4.

X^2/4 - Y^2/12 = 1

到两焦点距离之差为4