Express the parametric equation in form of y=f(x)

Question

I need to express the parametric equation in the form of $y=f(x)$ by eliminating the parameter.

I haven't learned how to do this yet, I've attempted to read a few pages though but they didn't help me much. Any advice and help is greatly appreciated!

$$c(t)=(1+t^{-1}, t^{2})$$

Answer 1

We are given that $(i): x = 1 + \frac{1}{t}$ and $(ii): y = t^{2}$:

From $(i): t = \frac{1}{x-1}$. Then it follows from $(ii)$ that $$y(x) = t^{2} = \frac{1}{(x-1)^{2}}$$