For hyperbola frac{{{x^2}}}{{{{cos }^2}α }} - frac{{{y^2}}}{{{{sin }^2}α }} = 1 which of following

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10-2. Parabola, Ellipse, Hyperbola

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For hyperbola $\frac{{{x^2}}}{{{{\cos }^2}\alpha }} - \frac{{{y^2}}}{{{{\sin }^2}\alpha }} = 1$ which of the following remains constant with change in $'\alpha '$

A

Abscissae of vertices

B

Abscissae of foci

C

Eccentricity

D

Directrix

(IIT-2003)

Solution

(b) $ae = \sqrt {{a^2} + {b^2}} = \sqrt {{{\cos }^2}\alpha + {{\sin }^2}\alpha } = 1$.

Standard 11

Mathematics

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