If the transverse and conjugate axes of a hyp | vedclass

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(B) Given that the transverse axis and conjugate axis of the hyperbola are equal.Let the equation of the hyperbola be $\frac{x^2}{a^2} - \frac{y^2}{b^

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$\sqrt{2}$

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(B) Given that the transverse axis and conjugate axis of the hyperbola are equal.Let the equation of the hyperbola be $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$.The length of the transverse axis is $2a$ and the length of the conjugate axis is $2b$.According to the problem,$2a = 2b$,which implies $a = b$.We know that for a hyperbola,$b^2 = a^2(e^2 - 1)$,where $e$ is the eccentricity.Substituting $b = a$ into the relation,we get $a^2 = a^2(e^2 - 1)$.Dividing both sides by $a^2$ (since $a 
eq 0$),we get $1 = e^2 - 1$.Therefore,$e^2 = 2$,which gives $e = \sqrt{2}$ (since eccentricity $e > 1$ for a hyperbola).

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

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