__Example__**: **Find an equation of the hyperbola with centre at origin, focus at and vertex at the point .

Since the focus of an ellipse lies on X-axis with centre , so let the required equation of hyperbola be

For hyperbola we have the relation

By the given conditions, we have

,

. Putting these values in the given condition of hyperbola, we get

Putting the values of

and

in the equation (i), we have

This is the required equation of hyperbola.

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