1. Implicit form

( x - x

_{0} )

^{2} + ( y - y

_{0} )

^{2} - R

^{2} == 0

Each pair {x,y} that fulfills the above equation is a point on the circle centered at (x

_{0},y

_{0}) and with radius R. AFAIK no rotation can be expressed within.

2. Parametric form

{ x = R cos( 2pi*t+p ), y = R sin( 2pi*t+p ) } w/ t in [0,1]

where a rotation in the given space can be expressed by varying the phase p.

3. Any form is given in a space, and the space can be rotated with the circle within and with respect to the reference space.

4. The (combined) visual representation of circle and line (i.e. a bitmap) can be rotated, what could be understood as a special case of 3. (kind of rotating in "pixel space").

However, as is written several times above, the visual representation will not change besides artifacts due to sampling. Demanding that the indicator line should not be rotated by itself because it would not be a proof that the circle rotates is senseless, because line and circle are 2 distinct objects anyway. That said, what sense does it make to rotate the circle in that way? Is the exercise correctly understood?