Question

The sum of the squares of the perpendiculars drawn onto any tangent to the ellipse x²/a² + y²/b² = 1 from the two points on the minor axis, each at a distance √(a² - b²) from the center, is

(a)   a²

(b)  1/2a²

(c)   3/2a²

(d)  2a²

Answer 1

Correct option (D)  2a²

Explanation  

We have

a² - b² = a² - a²(1 - e²)

= a²e²

Let P = (0, ae) and  Q = (0,-ae). Let p₁ and p₂ be the perpendiculars drawn from P and Q onto