Find the eccentricity of the hyperbola $9 y^{2} - 4 x^{2} = 36$ .

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Alok Kumar Singh | Contributor-Level 10

a year ago

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n e q u a t i o n i s 9 y^{2} - 4 x^{2} = 36 \\ \Rightarrow \frac{y^{2}}{4} - \frac{x^{2}}{9} = 36 \\ C l e a r l y i t i s v e r t i c a l h y p e r b o l a . \\ W h e r e a = 3 a n d b = 2 \\ N o w, b^{2} = a^{2} (e^{2} - 1) \\ \Rightarrow 4 = 9 (e^{2} - 1) \\ \Rightarrow e^{2} - 1 = \frac{4}{9} \Rightarrow e^{2} = 1 + \frac{4}{9} = \frac{13}{9} \\ ∴ e = \frac{\sqrt[]{13}}{3} \\ H e n c e, t h e r e q u i r e d v a l u e o f e i s \frac{\sqrt[]{13}}{3} . \end{array}$

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