Write the parametric equations of the circle $x^{2} + y^{2} - 2 x - 4 y - 4 = 0$

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Solution

$x^{2} + y^{2} - 2 x - 4 y - 4 = 0$
$x^{2} - 2 x + y^{2} - 4 y = 4$
$x^{2} - 2 x + 1 + y^{2} - 4 y + 4 = 4 + 1 + 4$
$(x - 1)^{2} + (y - 2)^{2} = 9$
$x - 1 = 3 cos θ, y - 2 = 3 sin θ$
$x = 1 + 3 cos θ, y = 2 + 3 sin θ$

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