Question

If the chords of contact of tangents from two points (x₁ ,y₁ ) and (x₂ ,y₂ ) to the ellipse x²/a² + y²/b² = 1 are at right angles then x₁x₂/y₂y₂   is equal to

(a)  a²/b²

(b)  -b²/a²

(c)  -a⁴/b⁴

(d)  -b⁴/a⁴

Answer 1

Correct option   (c)  -a⁴/b⁴

Explanation:

The equations of the chords of contact of tangents drawn from (x₁ ,y₁ ) and (x₂ ,y₂ ) to the ellipse x²/a² + b²/b² = 1 are

xx₁/a² + yy₁/b² = 1 .....(1)

and xx₂/a₂ + yy₂/b₂ = 1 ......(2)

It is given that (1) and (2) are at right angles product of their slopes is equal to –1.