Eccentricity of a hyperbola passing through points (3, 0) , (3√ 2 ,2) will be

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10-2. Parabola, Ellipse, Hyperbola

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The eccentricity of a hyperbola passing through the points $(3, 0)$, $(3\sqrt 2 ,\;2)$ will be

A

$\sqrt {13} $

B

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

C

$\frac{{\sqrt {13} }}{4}$

D

$\frac{{\sqrt {13} }}{2}$

Solution

(b) $\frac{9}{{{a^2}}} = 1$

==> $a = 3$ and $\frac{{18}}{{{a^2}}} – \frac{4}{{{b^2}}} = 1$

==> ${b^2} = 4$

Therefore, $e = \sqrt {1 + \frac{4}{9}} = \frac{{\sqrt {13} }}{3}$.

Standard 11

Mathematics

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