Write the v

Given:

Points O(0, 0), A(a cos θ, b sin θ) and (a cos θ, - b sin θ)

To find:

The value of for which area of the triangle formed by points O(0, 0), A(a cos θ, b sin θ) and (a cos θ, - b sin θ) is maximum.

Explanation:

Let A be the area of the triangle formed by the points O (0,0), A (acosθ, bsinθ) and B (acosθ, − bsinθ)

A

⇒ A

⇒ A = ab sinθcosθ

Now,
∴Amax, when sin2θ = 1

⇒ ∴Amax, when 2θ = π/2

⇒ θ

Hence, the area of the triangle formed by the given points is maximum when