The equation of the hyperbola whose conjugate | vedclass

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(A) Given,conjugate axis length $2b = 5 \implies b = \frac{5}{2}$.Distance between foci $2ae = 13 \implies ae = \frac{13}{2}$.For a hyperbola,we have

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

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(A) Given,conjugate axis length $2b = 5 \implies b = \frac{5}{2}$.Distance between foci $2ae = 13 \implies ae = \frac{13}{2}$.For a hyperbola,we have the relation $b^2 = a^2(e^2 - 1) = a^2e^2 - a^2$.Substituting the values: $(\frac{5}{2})^2 = (\frac{13}{2})^2 - a^2$.$\frac{25}{4} = \frac{169}{4} - a^2$.$a^2 = \frac{169}{4} - \frac{25}{4} = \frac{144}{4} = 36$.Thus,$a^2 = 36$ and $b^2 = \frac{25}{4}$.The standard equation of the hyperbola is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$.$\frac{x^2}{36} - \frac{y^2}{25/4} = 1$.$\frac{x^2}{36} - \frac{4y^2}{25} = 1$.Multiplying by $900$: $25x^2 - 144y^2 = 900$.

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

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