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Question

If the area bounded by the circle having centre at origin and radius 9 unit and the curve |x|+|y|=3 is aπ+b, then (a+b)= 


Solution

Equation of circle:x2+y2=92Equation of curve:|x|+|y|=3Points of contact:(0,9),(0,9),(9,0),(9,0)
As x increases, y decreases and vice-verse.
Required area=4[Shaded area in the first quadrant]
=4[π(9)2490(3x)2dx]=4[81π490(96x+x)dx]=81π54a=81, b=54a+b=8154=27

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