Question

y2(x-a)=x2 (x+a) the asymptotes are

Answer 1

How do I know how the graph should look like: For example: y2 = x - 2?

The first thing I recognize in that equation is the y2 term, which tells me it will be a parabola. (It won't be a circle, ellipse or hyperbola because there is an x term, but no x2 term. See Conic Sections.)

Let's start with the most basic parabola y = x2and build up to the required answer.