Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.

Question

x=4+2cos(theta) y=-1+2sin(theta)

Answer 1

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)