令抛物线为ρ=p/(1-cosθ)
MN的弦为θ=α
PQ的弦为θ=α+π/2
则有
a=p/(1-cosα)+p/(1-cos(π+α))=p/(1-cosα)+p/(1+cosα)=2p/(sinα)^2
b=2p/sin(α+π/2)^2=2p/(cosα)^2
1/a+1/b=1/2p=常量