The locus of the point which divides the double ordinates  of the ellipse x2a2+y2b2=1 in the ratio 1:2 internally is

Let P≡(acos⁡θ,bsin⁡θ),Q≡(acos⁡θ,−bsin⁡θ) .  PR:RQ=1:2∴ h=acos⁡θ or  cos⁡θ=ha----(1) and k=b3sin⁡θ or sin⁡θ=3kb----(2)On squaring and adding (i) and (ii), we getx2a2+9y2b2=1