The equation of the hyperbola whose conjugate | vedclass

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Question

(a) Conjugate axis is $5$ and distance between foci = $13$

==> $2b = 5$ and $2ae = 13$.

Now, also we know for hyperbola

${b^2} = {a^2}({e^

Vedclass · Accepted Answer

$25{x^2} - 144{y^2} = 900$

Vedclass · Answer

(a) Conjugate axis is $5$ and distance between foci = $13$

==> $2b = 5$ and $2ae = 13$.

Now, also we know for hyperbola

${b^2} = {a^2}({e^2} - 1)$

==> $\frac{{25}}{4} = \frac{{{{(13)}^2}}}{{4{e^2}}}({e^2} - 1)$

==> $\frac{{25}}{4} = \frac{{169}}{4} - \frac{{169}}{{4{e^2}}}$ or ${e^2} = \frac{{169}}{{144}}$

==> $e = \frac{{13}}{{12}}$

or $a = 6,\,b = \frac{5}{2}$ or hyperbola is $\frac{{{x^2}}}{{36}} - \frac{{{y^2}}}{{25/4}} = 1$

==> $25{x^2} - 144{y^2} = 900$.

The equation of the hyperbola whose conjugate axis is $5$ and the distance between the foci is $13$, is

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