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.