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

  • calculus -

    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)

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