A circle of radius 5 units touches the co-ordinates axes in first quadrant. If the circle makes one complete roll on x-axis along the positive direction of x-axis, find its equation in the new position.
None of these
Let C be the centre of the circle in its initial position and D be its centre in the new position.
Since the circle touches the co-ordinates axes in first quadrant and the radius of circle be 5 units.
∴ Centre of circle is (5, 5)
Moving length of circle = circumference of the circle
= 2πr = 2π (5) = 10π
Now centre of circle in new position is (5 + 10π, 5) and radius is 5 units, therefore, its equation will be
(x – 5 – 10π)2 + (y – 5)2 = 52
or x2 + y2 – 10(1 + 2π)x – 10y + 100π2 + 100π + 25 = 0
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