Question

Find the area of the region bounded by the curve y² = 2x and x² + y² = 4x.

Answer 1

Given equation of curves are y² = 2x and x² + y² = 4x

Solving the equations, we have

x² – 4x + y² = 0

x² – 4x + 4 – 4 + y² = 0

(x – 2)² + y² = 4

It’s clearly seen that the equation of the circle having its centre (2, 0) and radius 2.

Solving x² + y² = 4x and y² = 2x

x² + 2x = 4x

x² + 2x – 4x = 0

x² – 2x = 0

x(x – 2) = 0

So, x = 0, 2

Now, the area of the required region is given as