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Question -

Find the area of thecircle 4x2 + 4y2 = 9 which isinterior to the parabola x2 = 4y



Answer -

The required area isrepresented by the shaded area OBCDO.

Solving the givenequation of circle, 4x2 + 4y2 =9, and parabola, x2 = 4y, we obtain thepoint of intersection as.

It can be observed thatthe required area is symmetrical about y-axis.

Area OBCDO = 2 × AreaOBCO

We draw BM perpendicularto OA.

Therefore, thecoordinates of M are .

Therefore, Area OBCO = AreaOMBCO – Area OMBO

Therefore, the requiredarea OBCDO is units

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