1. 直线L: x/a+y/b=1
y1^2=2px1 ...(1), y2^2=2px2 ...(2)
x1/a+y1/b=1 ...(3), x2/a+y2/b=1 ...(4)
(3)-(4): (y1-y2)/(x1-x2)=-b/a
(1)-(2): (y1+y2)=-2ap/b ...(5)
(3)+(4): (x1+x2)/a +(y1+y2)/b =2 ...(6)
(1)+(2): (y1+y2)^2 -2*y1*y2 =2p(x1+x2) ...(7)
(5)(6)(7) ==> y1y2 = -2ap
1/y1 +1/y2 =(y1+y2)/(y1*y2) =(-2ap/b)/(-2ap) =1/b
2. y1/x1 =2p/y1, y2/x2 =2p/y2
当a=2p时:
(y1/x1)(y2/x2) =(2p/y1)(2p/y2) =4p^2/(y1y2)
= 4p^2/(-2ap) = -1
==> OM垂直ON