Found The Sides?

Let $P$ be a point on an ellipse $5x^2+9y^2=45$ with foci as $\text{S} _1$ and $\text{S}_2$ .

If area of $\Delta \text{S}_1\text{PS}_2$ is $4\text{ unit}^2$ , then find the ex radius of a circle of the triangle opposite to vertex $P$ .