The eccentricity of the hyperbola 4 x^2 - 9 y^2 = 16, is - Vidyadip

MCQ

The eccentricity of the hyperbola $4{x^2} - 9{y^2} = 16$, is

A
$\frac{8}{3}$
B
$\frac{5}{4}$
✓
$\frac{{\sqrt {13} }}{3}$
D
$\frac{4}{3}$

✓

Answer

Correct option: C.

$\frac{{\sqrt {13} }}{3}$

c
(c) Given equation of hyperbola, $\frac{{{x^2}}}{4} - \frac{{{y^2}}}{{(16/9)}} = 1$,

$a = 2,\,\,b = \frac{4}{3}$.

As we know, ${b^2} = {a^2}({e^2} - 1)$

==>$\frac{{16}}{9} = 4({e^2} - 1)$

==> ${e^2} = \frac{{13}}{9}$,

$\therefore e = \frac{{\sqrt {13} }}{3}$.

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