# Example of Finding Equation of Hyperbola

__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.