The area of the region, inside the ellipse x^2+4y^2=4 and outside the region bounded by the curves y= |x |-1 and y=1- |x |, is :

Question

Accepted Answer

Correct answer: D. (d) Ellipse: x^24+y^2=1 with a=2 ,b=1. Area = πab=2 . Curves y= |x |-1 and y=1- |x | intersect at x= 1, forming a rhombus with vertices (0 ,1 ) , (1 ,0 ) , (0 ,-1 ), (-1 ,0 ). Vertices (0 , 1 ) lie on ellipse; ( 1 ,0 ) are inside ellipse. Area of rhombus = 12 2 2=2. Required area =2 -2=2 ( -1 ).

$The area of the region, inside the ellipse x^{2} + 4 y^{2} = 4 and outside the region bounded by the curves y = | x | - 1 and y = 1 - | x |, is :$

Solution

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