Question

C is the centrec, AA' and BB' are major and minor axis of the ellipse. x2/a2 + y2/b2 = 1. If PN is the ordinate of a point P on the ellipse then show that (PN)2/(A'N)(AN) = (BC)2/(CA)2

Answer 1

Equation of the ellipse x2/a2 + y2/b2 = 1

P(a cos θ, b sin θ) any point on the ellipse.

PN = b sin θ; AN = a – a cos θ,

A'N = a + a cos θ ; BC = b, CA = a

(A'N). (AN) = (a + a cos θ) (a – a cos θ)

= a2 – a2 cos2 θ.

= a2 (1 – cos2 θ) = a2 sin2 θ