Mathematics

Problem

Let a tangent be drawn to the ellipse

\frac{x^2}{27}+y^2=1

(3\sqrt{3}\cos\theta,\sin\theta)

where

\theta \in \left(0, \frac{\pi}{2}\right)

. Then the value of

\theta

such that the sum of intercepts on axes made by this tangent is minimum is equal to: (a)

\frac{\pi}{8}

(b)

\frac{\pi}{4}

(c)

\frac{\pi}{6}

(d)

\frac{\pi}{3}