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

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Homework Help Overview

The problem involves parametric equations defined as x(t)=2t-1 and y(t)=t^2, with the goal of algebraically eliminating the parameter to derive a rectangular equation.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the method of isolating the parameter t from one equation and substituting it into the other. There is uncertainty about the process, particularly regarding the lack of examples in their textbook for non-trigonometric equations.

Discussion Status

Some participants have suggested isolating the parameter as a viable approach, while others express doubts about their understanding of the steps involved. There is ongoing exploration of the method without a clear consensus on the best approach.

Contextual Notes

Participants note the absence of examples in their textbook that specifically address the elimination of parameters in non-trigonometric contexts, which contributes to their uncertainty.

shauna_o
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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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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!
 
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.
 
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.
 

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