# Example of Finding Equation of Hyperbola

Example: Find an equation of the hyperbola with centre at origin, focus at $\left( {7,0} \right)$ and vertex at the point $\left( {3,0} \right)$.
Since the focus of an ellipse lies on X-axis with centre $\left( {0,0} \right)$, so let the required equation of hyperbola be

For hyperbola we have the relation

By the given conditions, we have $ae = 7$, $a = 3$. Putting these values in the given condition of hyperbola, we get

Putting the values of ${a^2}$ and ${b^2}$ in the equation (i), we have

This is the required equation of hyperbola.