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. $3(4-\pi)$

  2. $6(\pi-2)$

  3. $3(\pi-2)$

  4. $6(4-\pi)$


Correct Option: , 2

Solution:

$\frac{|x|}{2}+\frac{|y|}{3}=1$

$\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$

Area of Ellipse $=\pi a b=6 \pi$

Required area,

$=\pi \times 2 \times 3-($ Area of quadrilateral $)$

$=6 \pi-\frac{1}{2} 6 \times 4$

$=6 \pi-12$

$=6(\pi-2)$

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