If the eccentricity of the hyperbola is times the eccentricity of the ellipse

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

Problem

If the eccentricity of the hyperbola

x^2 - y^2 \sec^2 \alpha = 5

\sqrt{3}

times the eccentricity of the ellipse

x^2 \sec^2 \alpha + y^2 = 25

, then a value of

\alpha

is (1)

\frac{\pi}{6}

(2)

\frac{\pi}{4}

(3)

\frac{\pi}{3}

(4)

\frac{\pi}{2}