calculus
posted by ct .
Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.
x=4+2cos(theta) y=1+2sin(theta)

cosθ = (x4)/2
sinθ = (y+1)/2
(x4)^2 + (y+1)^2 = 4
it's easy to see why this drops out if you rewrite the original equations as
(x4) = 2cosθ
(y+1) = 2sinθ
So, it's the regular equation for a circle, but centered at (4,1) instead of (0,0)