# Math Help - Curve Tracing

1. ## Curve Tracing

The equation of the curve is- r^2cos2(theta)=q^2
Sorry I don't know to write this in Natural form but I just hope that I am clear enough

2. What are you supposed to do with this equation?

3. Originally Posted by stapel
What are you supposed to do with this equation?
Make the cure mate..

4. That's even more confusing!

And what is "q"? Some constant?

Do you know the identity " $cos(2\theta)= cos^2(\theta)- sin^2(\theta)$"? You can use that to write your equation as $r^2cos^2(\theta)- r^2sin^2(\theta)= q$ and use the fact that $x= r cos(\theta)$, $y= r sin(\theta)$ to change to Cartesian coordinates. Looks like a hyperbola to me.

5. Originally Posted by HallsofIvy
That's even more confusing!

And what is "q"? Some constant?

Do you know the identity " $cos(2\theta)= cos^2(\theta)- sin^2(\theta)$"? You can use that to write your equation as $r^2cos^2(\theta)- r^2sin^2(\theta)= q$ and use the fact that $x= r cos(\theta)$, $y= r sin(\theta)$ to change to Cartesian coordinates. Looks like a hyperbola to me.
Yes q is constant..!!
and the question is $r^2cos^2(\theta)- r^2sin^2(\theta)= q^2$ So I think it will be a rectangular hyperbola..??

6. Originally Posted by stapel
What are you supposed to do with this equation?
You have to make the curve with this. By making the curve I mean draw it by the equation
(I was told to give a direct answer to the question)