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

• Gundown64
In summary, the conversation is about eliminating the parameter t to find a Cartesian equation for a curve with the given conditions. The solution involves solving for t from y and substituting it into x, resulting in the equation y = ±√(1-x) - 3.
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

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.

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

## 1. What does "eliminate the parameter" mean?

Eliminating the parameter in a parametric equation means finding an equivalent equation that only has one independent variable, typically in terms of x and y.

## 2. How do I eliminate the parameter in a parametric equation?

To eliminate the parameter, you can solve for the parameter in one equation and substitute it into the other equation. This will result in an equation with only x and y as variables.

## 3. Why do we need to eliminate the parameter?

Eliminating the parameter can make it easier to graph the curve and find key points such as intercepts, maxima and minima, and points of inflection. It also allows us to write the equation in a familiar Cartesian form.

## 4. Can any parametric equation be converted to a Cartesian equation?

Yes, any parametric equation can be converted to a Cartesian equation by eliminating the parameter. However, some equations may result in complex or implicit forms.

## 5. Are there any limitations to eliminating the parameter?

Eliminating the parameter may not always give a complete description of the curve, as some important features may be lost in the process. Additionally, some parametric equations may not have a simple Cartesian form without resorting to advanced mathematical techniques.

Replies
6
Views
981
Replies
2
Views
3K
Replies
2
Views
914
Replies
1
Views
1K
Replies
1
Views
999
Replies
7
Views
881
Replies
16
Views
1K
Replies
1
Views
8K
Replies
2
Views
1K
Replies
3
Views
844