The area (in sq. units) of the region outside | vedclass

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(B) The given equations are $\frac{|x|}{2}+\frac{|y|}{3}=1$ (a rhombus) and $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$ (an ellipse).The area of the ellipse i

Vedclass · Accepted Answer

$6(\pi-2)$

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(B) The given equations are $\frac{|x|}{2}+\frac{|y|}{3}=1$ (a rhombus) and $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$ (an ellipse).The area of the ellipse is given by $A_{e} = \pi ab = \pi 	imes 2 	imes 3 = 6\pi$.The region $\frac{|x|}{2}+\frac{|y|}{3}=1$ represents a rhombus with vertices at $(\pm 2, 0)$ and $(0, \pm 3)$.The area of this rhombus is $A_{r} = \frac{1}{2} 	imes d_{1} 	imes d_{2} = \frac{1}{2} 	imes 4 	imes 6 = 12$.The required area is the area inside the ellipse but outside the rhombus,which is $A = A_{e} - A_{r} = 6\pi - 12 = 6(\pi - 2)$.

The 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

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