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10-2. Parabola, Ellipse, Hyperbola
medium
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