The following parametric equations define an ellipse. x=4cos(θ),y=5sin(θ),0≤θ≤2π Compute the area enclosed by this ellipse.

Answer 1

cosθ = x/4 and sinθ = y/5

Since cos²θ + sin²θ = 1, we have x²/16 + y²/25 = 1

a² = 25 and b² = 16

Area of ellipse = πab = 20π