finding cartesian equations of parametric equations

Question

find the Cartesian equation for the parametric equation $$x=\frac{1}{\sqrt{1-t}} \text{ and } y=\frac{t}{1-t}$$

I tried cross multiplying but I cant seem to find the equation in terms of $t$ to substitute.

Answer 1

Note that $$y = \frac{t}{1-t} = \frac{1-(1-t)}{1-t} = \frac{1}{1-t} - 1$$ and since $x = \frac{1}{\sqrt{1-t}}$ we have that $x^2 = \frac{1}{1-t} = y + 1$. So $y = x^2 - 1$ is the equation you're looking for.