Question

Let P be a variable point on the ellipse x2/a2 + y2/b2 = 1 with foci F1 and F2. If A is the area of the triangle PF1F2, then find the maximum value of A.

Answer 1

Given curve is x2/a2 + y2/b2 = 1

Let P(x, y) be any point and the foci are F1(– ae, 0) and F2(ae, 0) respectively.

Then the area of the triangle PF1F2

So A is maximum, when x = 0 and the maximum area = aeb = b√(a2 – b2).