If the transverse and conjugate axes of hyperbola are equal, then its eccentricity is

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Aicharya · Accepted Answer

Given that, transverse and conjugate axis of hyperbola are equal.

$C D \rightarrow$ transverse axis $A B \rightarrow$ conjugate axis $ \Rightarrow \quad 2 b=2 a \Rightarrow a=b $ Using equation of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ $ \left\{\because b^2=a^2\left(e^2-1\right)\right\} $ Now, $a^2=a^2\left(e^2-1\right) \Rightarrow e^2=2$ $ \Rightarrow \quad e=\sqrt{2} $

If the transverse and conjugate axes of hyperbola are equal, then its eccentricity is

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