Suppose S and S ′ are foci of the ellipse x 2 25 + y 2 16 = 1 . If P is a variable point on the ellipse and if ∆ is the area (in sq. units) of the triangle P S S ′ , then the maximum value of ∆ is double of

Step-by-step solution

Given , a 2 = 25 and b 2 = 16 ∴   e = 1 - b 2 a 2 = 1 - 16 25 =   3 5 So, the coordinates of foci S and S ′ are ( 3 ,   0 ) and ( - 3 ,   0 ) respectively. Let, P 5 cos ⁡ θ , 4 sin ⁡ θ be a variable point on the ellipse. Then, ∆ = a r e a   o f   ∆ P S S ′ = 1 2 3 0 1 - 3 0 1 5 cos ⁡ θ 4 sin ⁡ θ 1 = 12 sin ⁡ θ                         Since the