JEE Advance - Mathematics (1994 - No. 35)

Let $$P$$ be a variable point on the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ with foci $${F_1}$$ and $${F_2}$$. If $$A$$ is the area of the triangle $$P{F_1}{F_2}$$ then the maximum value of $$A$$ is ..........