Assertion (A): The ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ and the circle $x^{2} + y^{2} = 12$ enclose equal areas.

Reason (R): The area enclosed by $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is $\pi ab$.

Explanation

1. 01

   R: $\frac{4b}{a}\int_0^{a} \sqrt{a^{2} - x^{2}}\,dx = \pi ab$. True.

2. 02

   So the ellipse encloses $\pi \times 4 \times 3 = 12\pi$, and the circle, the case $a = b = \sqrt{12}$, encloses $12\pi$: A is true, and R explains it.