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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.
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Solution
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
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