Question

Eliminate the parameter. x = t + 4, y = t^2

Answer 1

We can do this by solving one of the equations for the parameter, and then substituting the result into the other equation; I'll use x to start:

\[x=t+4\]\[t=x-4\]

Now substitute into the other equation:
\[y=t^{2}\]\[y=(x-4)^{2}\]

We could also go the other way (start with y):
\[y=t^{2}\]\[t=\sqrt{y}\]
and substitute: \[x=t+4\]\[x=\sqrt{y}+4\]

We can check our work by solving this last equation for 'y' to see if we get the same equation as we did before:\[x=\sqrt{y}+4\]\[x-4=\sqrt{y}\]\[y=(x-4)^{2}\]

Since this is the same as what we got the first time, our answer checks out.