# State whether the following statement is True or False : If $P$ is a point the ellipse $\large\frac{x^2}{16}+\frac{y^2}{25}$$=1 whose foci are S and S',then PS+PS'=8. \begin{array}{1 1}\text{True}\\\text{False}\end{array} ## 1 Answer Comment A) Toolbox: • In an ellipse sum of the focal distances from the moving point P is 2b,where b is the distance between the centre and the vertex on the minor axis. Answer : False Given equation of the ellipse is \large\frac{x^2}{16}+\frac{y^2}{25}$$=1$
Hence $b^2=25$
$\Rightarrow b=\pm 5$
$\therefore PS+PS'=2b$
$\Rightarrow 2\times 5=10$