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

1. Mar 13, 2012

### 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.

1. The problem statement, all variables and given/known data
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

2. Relevant equations

N/A

3. 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.