Provide a parametrization with the given properties:
The curve is circled at point $(a, b)$. It is traced once counterclockwise, starting at the point $(a+r, b)$ with $t \in[0,2π]$
attempt:
$x = a + r cos(t), y = a+rsin(t)$ for $t \in [0, 2\pi]$
is above not right?
We have a circle of equation:
$$(x-a)^2+(y-b)^2=r^2$$
Setting $x=a+r\cos(t)$ and $y=b+r\sin t$ gives:
$$(r\cos(t))^2+(r\sin(t))^2=r^2$$
$$\to r^2(\cos^2(t)+\sin^2(t))=r^2$$
which holds because $\cos^2(t)+\sin^2(t)=1$
So your mistake was simply you need $y=b+...$ rather than $y=a+...$