Write 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.
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