Changing parametric equation to cartesian

Jul 2009
338
14
Singapore
I've got this parametric equations:
\(\displaystyle x=\frac{c(t^4+1)}{2t^3}\)
\(\displaystyle y=\frac{c(t^4+1)}{2t}\)
t is the variable
I am supposed to find the Cartesian equation of these points, are there any pointers like things to look out for when trying to convert such things? I want to try it myself, but i need some guidance as to where to start when dealing with such equations.
Thanks!
 

Grandad

MHF Hall of Honor
Dec 2008
2,570
1,416
South Coast of England
Hello arze
I've got this parametric equations:
\(\displaystyle x=\frac{c(t^4+1)}{2t^3}\)
\(\displaystyle y=\frac{c(t^4+1)}{2t}\)
t is the variable
I am supposed to find the Cartesian equation of these points, are there any pointers like things to look out for when trying to convert such things? I want to try it myself, but i need some guidance as to where to start when dealing with such equations.
Thanks!
It's difficult to define any hard-and-fast rules. Obviously, you have to eliminate \(\displaystyle t\) between the two equations, so you'll have to look for ways to do this. You could try to isolate \(\displaystyle t\) and then eliminate it by substitution.

In this case, the equations only differ in the power of \(\displaystyle t\) in the denominators on the right-hand-sides. So
\(\displaystyle y = t^2x\)
Now make \(\displaystyle t\) the subject of this equation, and eliminate it by substituting into whichever of the original equations looks like being the easier.

Grandad
 
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