The exercise is to find the parametric equation this curve: $x^2 + y^2 - 2x - 3 = 0$
So, I'm feeling pretty lost here and don't really know where to start. The process is explained poorly in my book with very few examples and can't find anything really useful online. So, I would really appreciate some help on how to tackle questions like this one.
hint
Observe that $$x^2-2x-3=(x-1)^2-4.$$
The curve equation can be written as
$$(x-1)^2+y^2=4=\color {red}{2}^2.$$
The parametrisation will be
$$x=1+\color {red}{2}\cos (t) $$ $$y=0+\color {red}{2}\sin (t) $$ with $ t\in [0,2\pi) $.
It is a circle of radius $r=\color {red}{2}$ and center $C (1,0) $.