I'm trying to determine the parametric equations of the path of a particle that travels the circle, on a time interval of $~0 \leq t \leq 2\pi$:
$$(x-5)^2 + (y-4)^2 = 100 $$
I have already solved the first two parts:
If that particle makes one full circles starting at the point (15,4) traveling counterclockwise:
$$x(t) = 5 + 10 \cos(t)~, \qquad y(t) = 4 + 10 \sin(t)$$
If that particle makes one full circle starting at the point (5,14) traveling clockwise:
$$x(t) = 5 + 10 \sin(t) ~, \qquad y(t) = 4 + 10 \cos(t)$$
However for the life of me I cannot figure out this one without changing the bounds:
if the particle makes one half of a circle starting at the point (15,4) traveling clockwise:
$$ x(t) = \text{?} ~, \qquad y(t) = \text{?}$$