How do I eliminate the parameter to find a Cartesian equation of the curve? (See problem below, please)

Question

anonymous · Answer

$\ \Huge x=t^2, y=6-3t $.

anonymous · Answer

here t=(6-y)/3
so x=((6-y)/5)^2

anonymous · Answer

So basically do you solve for t and then substitute that in to the next equation?

amistre64 · Answer

solve t in terms of x, and sub it into the y part

amistre64 · Answer

yes

anonymous · Answer

@amistre64 So, in this case t=sqrt(x), so I get $\ -3\sqrt{x}+6 ?$

anonymous · Answer

y= that is.

amistre64 · Answer

keep in mind the t^2 has 2 solutions; and that the true nature of the curve, if convention is followed, would result in 2 equations for y

but yes

anonymous · Answer

2 Equations?

amistre64 · Answer

$$t^2=x\to\ t=\pm\sqrt{x}$$
sub into y= to get:$$y=6\pm3\sqrt{x}$$

anonymous · Answer

That makes sense. Thank you, @amistre64!

amistre64 · Answer

youre welcome; matricks is fine to depending on how conventional they want the cartesian equation