Question

The circle x² + y² − 2x − 2y + 1 = 0 is rolled along the positive direction of x-axis and makes one complete roll. Find its equation in new-position.

Answer 1

Centre of the given circle = \[\left( 1, 1 \right)\]

Radius of the given circle = 1

This circle is rolled along the positive direction of the x-axis. When it makes one complete roll, its centre moves horizontally through a distance equal to its circumference, i.e 2 \[\pi\]

Thus, the coordinates of the centre of the new circle will be

\[\left( 1 + 2\pi, 1 \right)\]

Hence, the required equation of the circle is

\[\left( x - 1 - 2\pi \right)^2 + \left( y - 1 \right)^2 = 1\]