Question

A circle of radius 5 units touches both the axes and lies in first quadrant. If the circle makes one complete roll on x-axis along the positive direction of x-axis, then its equation in the new position is

• A. $x^{2} + y^{2} + 20\pi x - 10y + 100\pi^{2} = 0$
• B. $x^{2} + y^{2} + 20\pi x + 10y + 100\pi^{2} = 0$
• C. $x^{2} + y^{2} - 20\pi x - 10y + 100\pi^{2} = 0$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

The x-coordinate of the new position of the circle is 5 + circumferrence of the first circle $= 5 + 10\pi$

The y-coordinate is 5 and the radius is also 5.

Hence, the equation of the circle in the new position is $(x - 5 - 10\pi)^{2} + (y - 5)^{2} = (5)^{2} \Rightarrow x^{2} + 25 + 100\pi^{2} - 10x + 100\pi - 20\pi x + y^{2} + 25 - 10y = 25 \Rightarrow x^{2} + y^{2} - 20\pi x - 10x - 10y + 100\pi^{2} + 100\pi + 25 = 0$