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# Find the equations of the hyperbola satisfying the given conditions. Foci (± 5, 0), the transverse axis is of length 8.

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

Foci (± 5, 0), the transverse axis is of length 8.

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Given, in a hyperbola

Foci (± 5, 0), the transverse axis is of length 8.

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

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

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

$2a=8\Rightarrow a=4$ and $c=5$

Now, As we know the relation  in a hyperbola

$c^2=a^2+b^2$

$b^2=c^2-a^2$

$b^2=5^2-4^2$

$b^2=25-16=9$

Hence, The Equation of the hyperbola is ;

$\frac{x^2}{16}-\frac{y^2}{9}=1$

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