Find the area of the circle 4x² + 4y² = 9 which is interior to the parabola x² = 4y

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Solution

The required area is represented by the shaded area OBCDO.

Solving the given equation of circle, 4x² + 4y² = 9, and parabola, x² = 4y, we obtain the point of intersection as.

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

∴ Area OBCDO = 2 × Area OBCO

We draw BM perpendicular to OA.

Therefore, the coordinates of M are.

Therefore, Area OBCO = Area OMBCO – Area OMBO

Therefore, the required area OBCDO is units

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Similar questions

Find the area of the circle $4 x^{2} + 4 y^{2} = 9$ which is interior to the parabola $x^{2} = 4 y$

4 x^{2} + 4 y^{2} = 9

x^{2} = 4 y

{4 x}^{2} + {4 y}^{2} = 9

y^{2} = 4 x

4 x^{2} + 4 y^{2} = 9

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