• Support PF! Buy your school textbooks, materials and every day products Here!

Parametric equation

  • #1

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?

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:

Answers and Replies

  • #2
311
1
Solve for 't' in the first equation, and plug it in the second. Basically you have to eliminate 't'
 
  • #3
Disconnected
Gold Member
111
0
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))?
 
  • #4
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,219
945
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:
  • #5
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,219
945
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)
 

Related Threads for: Parametric equation

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
4
Views
1K
Top