Answer :

To find area of region{(x, y) : y2 3x, 3x2 + 3y2 16}

The given equations are,


y2 = 3x ...(i)


And 3x2 + 3y2 = 16


...(ii)


Equation (i) represents a parabola with vertex (0,0) and axis as x - axis,


Equation (ii) represents a circle with centre (0,0) and radius 4/√3 and meet at A and B A rough sketch of the region is drawn below



Required area = Region OCBAO


= 2(area of Region)


= 2(area of Region OBAO)


= 2(area of Region ODAO + area of Region DBAD)







The area enclosed by the region is


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