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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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