If transverse and conjugate axes of a hyperbola are equal, then its eccentricity is

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10-2. Parabola, Ellipse, Hyperbola

easy

If transverse and conjugate axes of a hyperbola are equal, then its eccentricity is

A

$\sqrt 3 $

B

$\sqrt 2 $

C

$1/\sqrt 2 $

D

$2$

Solution

(b) Hyperbola is $\frac{{{x^2}}}{{{a^2}}} – \frac{{{y^2}}}{{{b^2}}} = 1$.

Here, transverse and conjugate axis of a hyperbola is equal.

$i.e.$, $a = b$

$\therefore {x^2} – {y^2} = {a^2}$;

which is a rectangular hyperbola.

Hence, eccentricity $e = \sqrt {1 + \frac{{{b^2}}}{{{a^2}}}} = \sqrt 2 $.

Standard 11

Mathematics

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