Find the area bounded by curves (x – 1)² + y² = 1 and x² + y² = 1

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Solution

The area bounded by the curves, (x – 1)² + y² = 1 and x² + y² = 1, is represented by the shaded area as

On solving the equations, (x – 1)² + y² = 1 and x² + y² = 1, we obtain the point of intersection as Aand B.

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

∴ Area OBCAO = 2 × Area OCAO

We join AB, which intersects OC at M, such that AM is perpendicular to OC.

The coordinates of M are .

Therefore, required area OBCAO = units

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Similar questions

Find the area bounded by the curves $(x - 1)^{2} + y^{2} = 1$ and $x^{2} + y^{2} = 1$ .

| x | + | y | \geq 1

x^{2} + y^{2} \leq 1

(x - {1)}^{2} + y^{2} = 1

x^{2} + y^{2} = 1

x^{2} + y^{2} = 4, x^{2} = - \sqrt{2} y

x = y

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