Write the value of θε (0,π/2) 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.

Question

Write the value of θε \(\Big(0,\frac{\pi}{2}\Big)\) 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.

Answer 1

Given: 

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

To find:

The value of θε (0,\(\frac{π}{2}\))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)

Hence, the area of the triangle formed by the given points is maximum when θ = \(\frac{\pi}{4}\) .