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

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10-2. Parabola, Ellipse, Hyperbola

normal

For hyperbola $\frac{{{x^2}}}{{{{\cos }^2}\alpha }} - \frac{{{y^2}}}{{{{\sin }^2}\alpha }} = 1$ which of the following remain constant if $\alpha$ varies

Eccentricity

Directrix

Abscissae of vertices

Abscissae of foci

$\mathrm{a}^{2}=\cos ^{2} \alpha, \mathrm{b}^{2}=\sin ^{2} \alpha$

$e=\sqrt{1+\frac{b^{2}}{a^{2}}}=\frac{1}{\cos \alpha}$

Abscissa of foci $\equiv(a e, 0)=(1,0)$ which is independent of $\alpha .$

Standard 11

Mathematics

easy

hard

(JEE MAIN-2017)

medium

easy

easy