The area (in sq. units) of the region enclosed by the curve $9x^2 +4y^2 = 36$ is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6π
Given equation:
$9x^2 + 4y^2 = 36$
Divide through by 36:
$\frac{x^2}{4} + \frac{y^2}{9} = 1$
This represents an ellipse with:
$a^2 = 9 \Rightarrow a = 3$
$b^2 = 4 \Rightarrow b = 2$
Area of ellipse = $\pi a b = \pi (3)(2) = 6\pi$
Final Answer:
Area = $6\pi$ sq. units