Q84 / 150 · MHT CET 2019 (Shift 1) · Mathematics

The eccentricity of hyperbola $25 x^{2} - 9 y^{2} = 225$ is…

Correct answer
A
$\frac{\sqrt{34}}{3}$
B
4
C
$\sqrt{34}$
D
$\frac{\sqrt{34}}{5}$

Solution

We have equation of hyperbola

25 x^{2} - 9 y^{2} = 225

\Rightarrow \frac{x^{2}}{9} - \frac{y^{2}}{25} = 1

On comparing with

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

we get

a^{2} = 9, b^{2} = 25

∴

Eccentricity,

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

= \sqrt{1 + \frac{25}{9}}

= \frac{\sqrt{34}}{3}

Hence, the correct answer is option: 'A'.

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