If the tangent at the point of the hyperbola is parallel to

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

Problem

If the tangent at the point

(2\sec\phi, 3\tan\phi)

of the hyperbola

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

is parallel to

3x - y + 4 = 0

, then the value of

\phi

is (1)

\frac{\pi}{6}

(2)

\frac{\pi}{4}

(3)

\frac{\pi}{3}

(4)

\frac{5\pi}{12}