If P is a point on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ whose foci are $S, S\text{'}$ then $PS+PS\text{'}=$

Let $P\left(x_1,y_1\right)$ be a point on the ellipse $S=(ae,0),S^{\mathrm{\prime }}=(-ae,0)$

$\therefore SP/PM=e\Rightarrow SP=ePM=e\left(a/e-x_1\right)=a-x_{1}e$

Similarly $S^{\mathrm{\prime }}P=a+x_{1}e.\therefore SP+S^{\mathrm{\prime }}P=2a$