Prove that the length of perpendiculars from points `P(m^2,2m)Q(m n ,m+n)a n dR(n^2,2n)` to the line `x cos^2theta+ysinthetacostheta+sin^2theta=0` are in G.P.

Explanation

`p_1​=(m^2+2m+1)/sqrt(2)`

​`p-2​=(​mn+m+n+1)/sqrt(2)`

`​p_3​=(n^2+2n+1​)/sqrt(2)`

Then
`p_1​p_3​=p_2^2​`

⇒`p_1​,p_2​,p_3​` are in G.P