Solving Parametric Equations: Cartesian Equations from Parametric Equations

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Homework Help Overview

The discussion revolves around converting parametric equations into Cartesian form, specifically focusing on the elimination of the parameter 't' from the given equations. The subject area is primarily related to algebra and functions.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss methods for eliminating the parameter 't', including solving for 't' in one equation and substituting it into another. There are also considerations about the nature of Cartesian equations and whether the problem involves more complex relationships between variables.

Discussion Status

Some participants have offered guidance on potential methods for eliminating 't', while others are exploring the implications of the problem's structure. Multiple interpretations of the problem are being considered, indicating an active discussion without a clear consensus.

Contextual Notes

There are indications that the problem may involve additional complexities, such as handling different cases for 't' and ensuring the correct interpretation of the Cartesian form. The original poster has expressed uncertainty about how to proceed with the elimination process.

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Homework Statement



I have [PLAIN]http://img543.imageshack.us/img543/1608/msp481619fbgebbd2f2fg34.gif and [PLAIN]http://img153.imageshack.us/img153/121/msp69719fbh6if8c7b729c0.gif as my parametric equations with ''t'' as parameter. How to find its Cartesian equation?

Homework Equations





The Attempt at a Solution



I know i have to eliminate the ''t'', but i have no ideas how to eliminate it. Can anyone help me? Thanks...
 
Last edited by a moderator:
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Solve for 't' in the first equation, and plug it in the second. Basically you have to eliminate 't'
 
That fact that they say Cartesian makes me think that this is not just a y=f(x) question but a f(x,y) parametrized as f(t). Michael, is there more to the question that you posted?

Or is it just a case of finding t in terms of some f(x) and then replacing all of the t's in the y=g(t) to get y=f(g(x))?
 
Graph it on a graphing calculator. Nice Graph !

Let u = ln(t) for t > 0 → t = eu. (Take care of t < 0 later.)

The results for x&y should include cosh(u) & sinh(u) respectively.
 
Last edited:
Multiply the numerators & denominators of both expressions by 1/t.

[tex]x(t)=\frac{2at(1/t)}{3(t^2+1)(1/t)}=\frac{2a}{3(t+\frac{1}{t})}[/tex]

[tex]y(t)=\frac{-2bt(1/t)}{3(t^2-1)(1/t)}=\frac{-2b}{3(t-\frac{1}{t})}[/tex]

Therefore, x(1/t) = x(t) and y(1/t) = -y(t)
 

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