Tangents are drawn from the point to the ellipse touching the ellipse at points and

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

Problem

Tangents are drawn from the point

P(3, 4)

to the ellipse

\frac{x^2}{9} + \frac{y^2}{4} = 1

touching the ellipse at points

A

and

B

. What are the coordinates of

A

and

B

? (1)

(3, 0)

and

(0, 2)

(2)

\left(-\frac{8}{5}, \frac{2\sqrt{161}}{15}\right)

and

\left(-\frac{9}{5}, \frac{8}{5}\right)

(3)

\left(-\frac{8}{5}, \frac{2\sqrt{161}}{15}\right)

and

(0, 2)

(4)

(3, 0)

and

\left(-\frac{9}{5}, \frac{8}{5}\right)