Question

A circle of radius $5$ units touches the coordinate axes in the first quadrant. If the circle makes one complete roll on x-axis along the positive direction of x-axis, find its equation in new position.

Answer 1

Here $(5,5)$ is the center of circle which is touching both the coordinate axes in first quadrant and $5$ is the radius of circle, then $(x-5{)}^2+(y-5{)}^2=5^2.$ is the equation of the circle

Now it makes one complete roll along positive $X$ axis,hence its $x$ coordinate of center will change its position to $5+10\pi$ while $y$ coordinate will remain the same.

$\therefore$ The final equation will be,$(x-(5+10\pi ){)}^2+(y-5{)}^2=5^2.$