- #1
LostInSpace
- 21
- 0
Hi all! I'm having some problems with parametrization. I read somewhere that you should locate circles, ellipses, hyperboloides, paraboloides etc and use these elements to express a parametric function.
But someone must have figured out how to do it! The way I see it, there's nothing logical about
[tex]
x^2+y^2-z^2=1 \Leftrightarrow f(t,\varphi)=\left(\sqrt{t^2+1}\cos\varphi,\sqrt{t^2+1}\sin\varphi,t\right)
[/tex]
Yes, I understand that
[tex]
(\sqrt{t^2+1}\cos\varphi)^2 + (\sqrt{t^2+1}\sin\varphi)^2 - t^2 = 1
[/tex]
but how do you actually get to that conclusion (without plotting the function)?
Consider this problem (which may be simple):
Determine the intersecting curve (parametric function) between the surfaces [tex]z^2=x^2+y^2[/tex] and [tex]z=x+y[/tex]. How do you approach that?
Thanks in advance!
But someone must have figured out how to do it! The way I see it, there's nothing logical about
[tex]
x^2+y^2-z^2=1 \Leftrightarrow f(t,\varphi)=\left(\sqrt{t^2+1}\cos\varphi,\sqrt{t^2+1}\sin\varphi,t\right)
[/tex]
Yes, I understand that
[tex]
(\sqrt{t^2+1}\cos\varphi)^2 + (\sqrt{t^2+1}\sin\varphi)^2 - t^2 = 1
[/tex]
but how do you actually get to that conclusion (without plotting the function)?
Consider this problem (which may be simple):
Determine the intersecting curve (parametric function) between the surfaces [tex]z^2=x^2+y^2[/tex] and [tex]z=x+y[/tex]. How do you approach that?
Thanks in advance!