Area (in sq. units) of the region outside
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 :

 

  1. (1) $6(\pi-2)$

  2. (2) $3(\pi-2)$

  3. (3) $3(4-\pi)$

  4. (4) $6(4-\pi)$


Correct Option: 1

Solution:

$-4$ (Area of triangle OPQ)

$=6 \pi-4\left(\frac{1}{2} \times 2 \times 3\right)$

$=6 \pi-12=6(\pi-2)$ sq. units

 

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