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Find the equations of the hyperbola satisfying the given conditions.Vertices (0, ± 5), foci (0, ± 8)

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

       Vertices (0, ± 5), foci (0, ± 8)

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Given, in a hyperbola

Vertices (0, ± 5), foci (0, ± 8)

Here, Vertices and 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 (Vertices and foci) with the given one, we get

a=5 and c=8

Now, As we know the relation  in a hyperbola 

c^2=a^2+b^2

b^2=c^2-a^2

b^2=8^2-5^2

b^2=64-25=39

Hence, The Equation of the hyperbola is ;

\frac{y^2}{25}-\frac{x^2}{39}=1.

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