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

Question

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)

Answer 1

The correct answer is option c) 6(\(\pi-2\)) 

Explaination::

 

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)