Coordinate geometry is more about straight lines usually (y = mx + b) or points on the x, y coordinate system.
However, it is good to know that a parabola comes from the fact that if you have a squared term, (x squared or y squared) then this means you will have two points on one axis for each point on the other. So parabolas are not common but you will just want to know what type of equation causes them.
No need for coordinate geometry to be that scary since it is limited in scope. In fact, all of geometry is a bit limited to common shapes and formulas.