以F為極點(diǎn),垂直于l且過F的直線為極軸建立坐標(biāo)系.
設(shè)N(L1,θ)、M(L2,θ+π) (-π/2<θ<π/2).
故L2*cos(θ+π)=-L →L2=p/cosθ
又,|FN|/|MN|=1/|MF|
即L1*L2=L1+L2,
∴L1=L2/(L2-1)=L/(L-cosθ),故
L1+L2
=p/cosθ+p/(p-cosθ)
=p^2/[cosθ(p-cosθ)]
≥p^2/(p^2/4)
=4.
取等號(hào)條件為cosθ=p/2時(shí)取得:
(1)若0(2)若P>2,則當(dāng)cosθ=1時(shí),L1+L2取得最小值為p^2/(p-1).