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Find the equations of the hyperbola satisfying the given conditions.Vertices (± 2, 0), foci (± 3, 0)

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

       Vertices (± 2, 0), foci (± 3, 0)

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Given, in a hyperbola

Vertices (± 2, 0), foci (± 3, 0)

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

a=2 and c=3

Now, As we know the relation  in a hyperbola 

c^2=a^2+b^2

b^2=c^2-a^2

b^2=3^2-2^2

b^2=9-4=5

Hence,The Equation of the hyperbola is ;

\frac{x^2}{4}-\frac{y^2}{5}=1

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