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

  1. Mar 13, 2012 #1
    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−[itex]t^{2}[/itex], 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 [itex]\sqrt{1-x}[/itex]. Then I plugged it into y=t-3 and got y=[itex]\sqrt{1-x}[/itex]-3. However, that only gives me half of the parabola when I graph it. I know I need y=-[itex]\sqrt{1-x}[/itex]-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!
     
    Last edited: Mar 13, 2012
  2. jcsd
  3. Mar 13, 2012 #2
    instead of solving t from x, try solving t from y and sub into x.
     
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