If chords of contact of tangents from two points and to the ellipse are at right angles

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

If chords of contact of tangents from two points

(x_1, y_1)

and

(x_2, y_2)

to the ellipse

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

are at right angles, then

\frac{x_1 x_2}{y_1 y_2}

is equal to (1)

\frac{a^2}{b^2}

(2)

-\frac{b^2}{a^2}

(3)

-\frac{a^4}{b^4}

(4)

-\frac{b^4}{a^4}