The area (in sq. units) of the region enclosed by the curve $9x^2 +4y^2 = 36$ is

6π

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