# Parametric equation

## Homework Statement

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

## 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...

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Solve for 't' in the first equation, and plug it in the second. Basically you have to eliminate 't'

Disconnected
Gold Member
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))?

SammyS
Staff Emeritus
Homework Helper
Gold Member
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.

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SammyS
Staff Emeritus
Homework Helper
Gold Member
Multiply the numerators & denominators of both expressions by 1/t.

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

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

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