Question

Find the maximum area of an isosceles triangle inscribed in the ellipse x2/a2 +y2+b2=1 with its vertex at one end of the major axis.

Answer 1

The given ellipse is

Let the major axis be along the x −axis.
Let ABC be the triangle inscribed in the ellipse where vertex C is at (a, 0). Since the ellipse is symmetrical with respect to the x−axis and y −axis, we can assume the coordinates of A to be (−x1, y1) and the coordinates of B to be (−x1, −y1).

As the point (x1, y1) **** on the ellipse, the area of triangle ABC (A) is given by,

But, x1 cannot be equal to a.