posted by ct .
Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.
cosθ = (x-4)/2
sinθ = (y+1)/2
(x-4)^2 + (y+1)^2 = 4
it's easy to see why this drops out if you rewrite the original equations as
(x-4) = 2cosθ
(y+1) = 2sinθ
So, it's the regular equation for a circle, but centered at (4,-1) instead of (0,0)