已知直线l过定点（0,3）,且是曲线y²=4x的动弦P1P2的中垂线,求直线l与动弦P1P2的交点M的轨迹方程

直线L过定点A（0,3)
曲线C:y^2= 4x
设 P(x,y),P(x1,y1),P2(x2,y2)
P 是P1P2中点,=>
x1+x2 = 2x,y1+y2=2y
P1,P2 在 C上,有
y1^2=4x1 and y2^2=4x2
=> 4(x2-x1)= y2^2-y1^2
=> (y2-y1)/(x2-x1) = 4/(y2+y1)
=> (y2-y1)/(x2-x1) = 4/2y
AP斜率 = (y-3)/x
P1P2斜率 = (y2-y1)/(x2-x1)
AP 垂至于P1P2 => KAP *KP!P2 = -1 =>
((y-3)/x) ( y2-y1)/(x2-x1) = -1
((y-3)/x) (4/2y) = -1
2(y-3) = -xy
xy-2y-6 = 0
求直线L与动弦p1p2的交点M的轨迹方程:
xy-2y-6 = 0