Question

If the tangents form the point $(\lambda ,3)$ to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ are at right angles, then $\lambda$ =

• A. $\pm 1$
• B. $\pm \sqrt{3}$
• C. $\pm 2$
• D. $\pm 3$

Answer 1

The correct option is C

$\pm 2$

Since the tangents are at right angles. Point $(\lambda ,3)$ lies on the director circle, $x^2+y^2=13$

$\therefore {\lambda }^2+9=13\Rightarrow \lambda =\pm 2$