Eliminate the parameter to find a Cartesian equation of the curve.

[Gundown64]

EDIT: Figured it out. Stupid me. I should have solved in terms of x, giving me x=1-(y+3)^2 as my answer.

Homework Statement

x= 1−t^{2}, y= t−3, −2 ≤ t ≤ 2

Eliminate the parameter to find a Cartesian equation of the curve for
−5 ≤ y ≤ −1

Homework Equations

N/A

The Attempt at a Solution

I solved for t and got \sqrt{1-x}. Then I plugged it into y=t-3 and got y=\sqrt{1-x}-3. However, that only gives me half of the parabola when I graph it. I know I need y=-\sqrt{1-x}-3 to get the other half, but how do I make that one equation. I don't think I can use a ± sign in my answer.

Thanks in advance!

 

[sunjin09]

instead of solving t from x, try solving t from y and sub into x.