<s>[INST] Parametric question of the curve $x^2 + y^2 + 2x - 4y = 0$? What is the parametric form of the curve above?  If I had to solve it, what I would say is that the first step is to complete the square. However, where would I go from there?
 [/INST] $$x^2 + y^2 + 2x - 4y = 0$$
$$x^2  + 2x +  y^2- 4y = 0$$
$$x^2  + 2x +  1 -1 +y^2- 4y +4 -4= 0$$
$$(x+1)^2 -1 + (y-2)^2-4= 0$$
$$(x+1)^2  + (y-2)^2= 5$$
For a circle with centre at (h,k) and radius r, the a parametric form is $x = h + r\cos(\theta)$ and $y = k + r\sin(\theta)$.
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