Parametric equation for y^2 = x+1

Question

How do you parametrise $$y^2 = x+1$$ ?

I only know how to parametrise a circle.

Answer 1

There are many options

For example

Set $y=t$. so that $x=t^2-1$ simplest, right?

Or $y=p+1,x=(p+1)^2-1$

Answer 2

I would use $$y=tx$$ so we get $$x^2-\frac{1}{t^2}x-\frac{1}{t^2}=0$$ and we get $$x_{1,2}=-\frac{1}{2t^2}\pm\sqrt{\frac{1}{4t^4}+\frac{1}{t^2}}$$