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.(adsbygoogle = window.adsbygoogle || []).push({});

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!

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# Problems with parametrization

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