The correct option is D x2a2+y2b2=12
Given ellipse is x2a2+y2b2=1
Let P≡(acosθ,bsinθ), then
D≡(acos(θ+π2),bsin(θ+π2))
⇒D≡(−asinθ,bcosθ)
Let mid point of PD be M(h,k)
So, h=acosθ−asinθ2
⇒cosθ−sinθ=2ha …(1)
And
k=bsinθ+bcosθ2
⇒sinθ+cosθ=2kb …(2)
Squaring and adding equation (1) and (2)
⇒2sin2θ+2cos2θ+2sinθcosθ−2sinθcosθ=(2ha)2+(2kb)2
⇒2=(2ha)2+(2kb)2
⇒x2a2+y2b2=12