Question

A circle of radius $5$ units touches both the axes and lies in the first quadrant. If the circle makes one complete revolution 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

The correct option is D None of these

Coordinates of centre of the circle is $C(5,5)$
After one roll (revolution) (along the positive direction of x-axis), the x-coordinate of centre be original radius $+$ distance covered in one roll i.e. $2\pi r$ and y-coordinate of centre be same
$\therefore$ Centre of the circle in new position is $C(5+10\pi ,5)$
$\therefore$ Equation of circle is $(x-5-10\pi {)}^2+(y-5{)}^2=5^2$
Which does not match with any choice.
Hence choice (d) is correct answer.