# Find the maximum area of $\Delta PSS'$ for the ellipse $\large\frac{x^2}{36}+\frac{y^2}{16}$$=1 where S,S' are foci & P is any point on ellipse? \begin{array}{1 1}(a)\;8\sqrt 6\\(b)\;8\sqrt 2\\(c)\;8\sqrt 5\\(d)\;\text{None of these}\end{array} ## 1 Answer a^2=36 b^2=16 \large\frac{b^2}{a^2}$$=1-e^2$
$\large\frac{16}{36}$$-1=-e^2 \large\frac{20}{36}$$=-e^2$
$e=\large\frac{2\sqrt 5}{6}$
$e=\large\frac{\sqrt 5}{3}$
For maximum area of $\Delta PSS'$ P should be one of the vertex of minor axis hence