Given the two parametric equations


$$y=t+1 \iff t= y-1$$

How do I eliminate parameter $t$ to find a Cartesian equation? Do I substitute?

This is confusing me, so I would appreciate it if somebody could explain how to do this. Thank you for your time.

  • 1
    $\begingroup$ You can get $t$ from $s$ also. Then eliminate $t$ from the two relations. $\endgroup$ – Narasimham Dec 10 '18 at 21:59

Both $x$ and $y$ are functions of $t$.

Solving $y = t+1$ to obtain $t$ as a function of $y$: we have $t = y-1.\quad$

So given $x=t^2 + 1$, by substitution of $t = (y-1)$, we have $$x=(y-1)^2 +1 \iff x-1=(y-1)^2$$

We have a horizontal parabola with vertex at $(1, 1)$ and opening to the right (positive direction.)


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