Find a parameterization for a circle

Question

Find a parameterization for the circle (x-10)^(2) + y^(2)= 25 starting at the point (5,0) and moving clockwise once around the​ circle, using the central angle θ in the figure to the right as the parameter.

x=____ y=____ , 0 ≤ θ ≤ 2pi

Answer 1

Given the equation (x-10)² + y² = 25, we will need the parametrization equations for circles not centered about the origin:

x = h + rcos(θ)

y = k + rsin(θ)

in which (h,k) is the center of the circle and r is the radius. The center of our circle is at (10,0) so we plug this in for (h,k), and our radius is √25 = 5. Our equations are then

x = 10 + 5cos(θ)

y = 5sin(θ)

for all θ such that 0 ≤ θ ≤ 2π