Q. Area enclosed by the curve $\pi\lbrack 4\left( x - \sqrt{2})^{2} + y^{2} \right\rbrack = 8$ is
A) $\pi\ sq\ units\$
B) $2\ sq\ units\$
C) $3\pi\ sq\ units\$
D) 4 $sq\ units$
Explanation
(d)
The given equation can be rewritten as
$\frac{(x - \sqrt{2})^{2}}{2/\pi} + \frac{y^{2}}{8/\pi} = 1$
Which represent an ellipse.
$Here,\ \ \ a = \sqrt{\frac{2}{\pi}}$
$and\ \ \ b = \sqrt{\frac{8}{\pi}}$
Area enclosed by an ellipse$= \pi ab$
$= \pi\sqrt{\frac{2}{\pi}}\sqrt{\frac{8}{\pi}}$
$= 4\ sq\ units$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.