1. Tardigrade
  2. Question
  3. Mathematics
  4. The area enclosed by the curve x=3 cos θ, y=2 sin θ, 0 ≤ θ ≤ π, is (in square units)

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The area enclosed by the curve $x=3 \cos \theta, y=2 \sin \theta, 0 \leq \theta \leq \pi$, is (in square units)

KEAMKEAM 2020

Solution:

$\frac{x}{3}=\cos \theta$
$\frac{y}{2}=\sin \theta$
$\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$
$\Rightarrow $ (curve is ellipse in first and 2nd quadrant)
area $=\frac{\pi a b}{2}$
$=\frac{\pi+3 \times 2}{2}=3 \pi$