Solving Parametric Equations: x(t)=2t-1 & y(t)=t^2

In summary, To convert from parametric to Cartesian, you must eliminate the parameter by isolating it and substituting it into the other equation. In this case, t can be solved for in the first equation, and then substituted into the second equation to create a rectangular equation.
  • #1
shauna_o
2
0

Homework Statement


x(t)=2t-1
y(t)=t^2

algebraically eliminate the parameter to create a rectangular equation


Homework Equations



There was an example in our book that showed how to do this if the two equations contained sine and cosine, however nothing was said if they didn't. I don't even know where to start?
 
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  • #2
I've been working with this problem still, and was wondering if i was on the right track...

to solve for the parameter i have to isolate the T and then subsitute into the other problem?

hopefully that's correct, but i'd love if someone could let me know. thanks!
 
  • #3
shauna_o said:
I've been working with this problem still, and was wondering if i was on the right track...

to solve for the parameter i have to isolate the T and then subsitute into the other problem?

hopefully that's correct, but i'd love if someone could let me know. thanks!


To convert from parametric to Cartesian, you must eliminate the parameter. So,yes, that is the way to go.
 
  • #4
x(t)=2t-1
y(t)=t2

From the first equation 2t- 1= x so 2t= x+1 and t= (x+1)/2. Replace t in the second equation by that.
 

1. What are parametric equations?

Parametric equations are a set of equations that express the coordinates of points on a curve or surface in terms of one or more independent variables, known as parameters.

2. How do I solve parametric equations?

To solve parametric equations, you must find a relationship between the two equations and eliminate the parameter. This can be done by substituting the parameter from one equation into the other and solving for the remaining variable.

3. What does x(t) and y(t) represent in parametric equations?

x(t) and y(t) represent the coordinates of a point on the curve or surface at a specific value of the parameter t. The value of t can be thought of as the time or a specific moment on the curve or surface.

4. How many solutions are there to a set of parametric equations?

There can be infinitely many solutions to a set of parametric equations, as the values of t can vary continuously and produce different points on the curve or surface.

5. Can parametric equations be graphed?

Yes, parametric equations can be graphed by plotting points on a coordinate plane using different values of the parameter t. This produces a parametric curve or surface, which can have different shapes depending on the equations.

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