Prove that the chord of contact of tangents drawn from the point to the ellipse will…

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Prove that the chord of contact of tangents drawn from the point

(h, k)

to the ellipse

\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

will subtend a right angle at the centre, if

\frac{h^2}{a^4} + \frac{k^2}{b^4} = \frac{1}{a^2} + \frac{1}{b^2}

. Also, find the locus of

(h, k)