過(guò)拋物線y^2=4x的焦點(diǎn)F作一直線交拋物線于P,Q兩點(diǎn),若線段PF與FQ的長(zhǎng)分別是p、q,則1/p+1/q等于?
F(1,0)
則是y-0=k(x-1)
y=kx-k
代入
(kx-k)²=4x
k²x²-(2k²+4)x+k²=0
x1+x2=(2k²+4)/k²
x1x2=1
準(zhǔn)線x=-1
拋物線定義
PF=P到準(zhǔn)線距離
所以p=x1+1.q=x2+1
1/p+1/q
=1/(x1+1)+1/(x2+1)
=(x1+x2+2)/(x1x2+x1+x2+1)
=[(2k²+4)/k²+2]/[1+(2k²+4)/k²+1]
=[(2k²+4)/k²+2]/[(2k²+4)/k²+2]
=1