Consider the circle of radius $1$ unit with its centre at the point $(0,1)$. From the initial position, the circle is rolled along the positive $x$- axis without slipping. Find the locus of the point $P$ on the circumference of the circle which is on the origin at the initial position of the circle.
I had been trying to calculate position of point after circle moves t units but to no avail. Any help will be very helpful.