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# Find the equations of the hyperbola satisfying the given conditions. Vertices (0, ± 3), foci (0, ± 5)

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

Vertices (0, ± 3), foci (0, ± 5)

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Given, in a hyperbola

Vertices (0, ± 3), foci (0, ± 5)

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

$a=3$ and $c=5$

Now, As we know the relation  in a hyperbola

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

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

$b^2=5^2-3^2$

$b^2=25-9=16$

Hence, The Equation of the hyperbola is ;

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

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