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  4. Area (in sq. units) of the region outside (|x|/2)+(|y|/3)=1 and inside the ellipse (x2/4)+(y2/9)=1 is:

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Q. 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:

JEE MainJEE Main 2020Conic Sections

Solution:

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