1. ## Need help with Parametric Represntation Please

The problem:
Consider the curve x^2+xy+y^2=3
1. Show that a parametic representation of the above curve is:
------{x=cost - (3)^(1/2)sint
------{y=cost +(3)^(1/2)sint
2. Use this parametric representation to find the slope of the tangent to the curve at (1,1) (t=0).

So far I have this work:
For x --> x^2+xsint+sint^2=3
==> xsint+sint^2=3 - x^2
==> (sint)(x+sint)=3 - x^2
==> ?
For y ---> cost^2+ycost+y^2=3
==> ycost+cost^2=3 - y^2
==> (cost)(x+cost)=3 - y^2
==> ?

I don't know where to go from there and what to do. Can someone please help me?

2. I don't think there is anything wrong with the second part. But I believe that I am trying to prove that with parametric representation x^2+xy+y^2=3 is equal to: x=cost - (3)^(1/2)sint and y=cost +(3)^(1/2)sint. And I was wondering if anyone could help me with that. Also I do not know if they will reply back to answer that. And I try to get help from several sources so that hopefully I will be able to understand it one way that is posted.

3. Originally Posted by Calaghan
I don't think there is anything wrong with the second part. But I believe that I am trying to prove that with parametric representation x^2+xy+y^2=3 is equal to: x=cost - (3)^(1/2)sint and y=cost +(3)^(1/2)sint. And I was wondering if anyone could help me with that. Also I do not know if they will reply back to answer that. And I try to get help from several sources so that hopefully I will be able to understand it one way that is posted.
What they did on the other site (and all you need to do) is plug the x(t) and y(t) equations into $\displaystyle x^2+xy+y^2=3$ and verify that the equation is correct. There is no actual "derivation" as such that will give you these forms for x(t) and y(t). (In fact there are almost certainly any number of distinct ways to break the solution into a parametric representation.)

-Dan