﻿ 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. : Kaysons Education

# 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.

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## Question

### Solution

Correct option is

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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