Question

If the normal at the point P(θ) to the ellipse x²/14 +y²/5 = 1 intersects it again at the point Q(2θ), show that cos θ = -(2/3).

Answer 1

 Normal at P(θ) is 

ax secθ – bycosecθ = a² – b² 

It passes through Q(acos²θ, bsin²θ)