Answer :

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

The given equations are,

y2 = 3x ...(i)

And 3x2 + 3y2 = 16


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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