Find the parametric equations of the circle $x^{2} + y^{2} - 4 x - 2 y + 1 = 0$

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Solution

We have $x^{2} + y^{2} - 4 x - 2 y + 1 = 0$
$\Rightarrow (x^{2} - 4 x) + (y^{2} - 2 y) = - 1$
$\Rightarrow {(x - 2)}^{2} + {(y - 1)}^{2} = 2^{2}$
So the parametric equations of this circle are
$x = 2 + 2 cos θ, y = 1 + 2 sin θ$

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