Q: Equation of tangent to two ellipse $\large \frac{x^2}{9} + \frac{y^2}{4} = 1$ which cut off equal intercepts on the axes is

(A) $ y = x + \sqrt{13}$

(B) $ y = -x + \sqrt{13}$

(C) $ y = x – \sqrt{13}$

(D) $ y = -x – \sqrt{13}$

Sol. Equation of tangent to ellipse $\large \frac{x^2}{9} + \frac{y^2}{4} = 1$ is

$\large y = mx \pm \sqrt{9m^2 + 4} $

Here m = ± 1

⇒ tangents are $ y = \pm x \pm \sqrt{13}$