y^2=4x
焦點(diǎn)F(p/2,0)
準(zhǔn)線x=-p/2
設(shè)焦點(diǎn)弦:y=tanα*(x-p/2) (α≠π/2)
y=tanα*(x-p/2)代入y^2=2px
(tanα)^2x^2-[(tanα)^2+2]px+(ptanα)^2/4=0
由根與系數(shù)關(guān)系
x1+x2=p[(tanα)^2+2]/(tanα)^2=[1+2/(tanα)^2]p
由拋物線上任意一點(diǎn)到焦點(diǎn)距離與到準(zhǔn)線距離相等
|AB|=|AF|+|BF|
=|x1+p/2|+|x2+p/2|
=x1+x2+p
=2p[1+1/(tanα)]^2
=2p[1+(cotα)^2]
=2p(cscα)^2
=2p/(sinα)^2
當(dāng)AP傾斜角為π/2時(shí)
|AB|=2p=2p/[sin(π/2)]^2
可知|AB|=2p/(sinα)^2