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Area (in sq. units) of the region outside \({|x|\over2}+{|y|\over3}=1\) and inside the ellipse \({x^2\over4}+{y^2\over9}=1\) is


(a) 3(π – 2)
(b) 3(4 – π)
(c) 6(π – 2)
(d) 6(4 – π)
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The correct answer is option c) 6(\(\pi-2\)

Explaination::
img

 

Area of Ellipse =πab=6π

Area \({|x|\over2}+{|y|\over3}=1\) is 

 \(={1\over2}(d_1d_2)={1\over2}(4)(6)=12\)  

 

so   Area is =6π−12=6(π−2)

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