Question

Area (in sq. units) of the region outside $\frac{|x|}{2}+\frac{|y|}{3}=1$ and inside the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ is:

• A. $3(4-\pi )$
• B. $6(\pi -2)$
• C. $3(\pi -2)$
• D. $6(4-\pi )$

Answer 1

Answer: (B)

$\frac{|x|}{2}+\frac{|y|}{3}=1$
$\frac{x^2}{4}+\frac{y^2}{9}=1$
Area of Ellipse $=\pi ab=6\pi$
Required area,
$=\pi \times 2\times 3-$ (Area of quadrilateral)
$=6\pi -\frac{1}{2}6\times 4$
$=6\pi -12$
$=6(\pi -2)$