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Find the equations of the hyperbola satisfying the given conditions. Foci (0, ±13), the conjugate axis is of length 24.

11.  Find the equations of the hyperbola satisfying the given conditions.

       Foci (0, ±13), the conjugate axis is of length 24.

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Given, in a hyperbola

Foci (0, ±13), the conjugate axis is of length 24.

Here, focii are on the Y-axis so, the standard equation of the Hyperbola will be ;

\frac{y^2}{a^2}-\frac{x^2}{b^2}=1

By comparing the standard parameter (length of conjugate axis and foci) with the given one, we get

2b=24\Rightarrow b=12 and c=13

Now, As we know the relation  in a hyperbola 

c^2=a^2+b^2

a^2=c^2-b^2

a^2=13^2-12^2

a^2=169-144=25

Hence, The Equation of the hyperbola is ;

\frac{y^2}{25}-\frac{x^2}{144}=1.

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