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I have a curve given by this equation: $$c(t) = (t\cos t,t \sin t,t)$$

I need to prove that this curve lies on a cone, and draw that cone and curve in Sage.

I've read somewhere that I could prove it by taking some random point and then put it into equation. But is there a more general proof, formal way of proving it lies on a cone?

How should I prove it (the easiest way?)

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    It's obvious that $z^2=x^2+y^2$ and that's the equation of a (double) cone.2012-05-20
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    @kiwi Can you add that as answer so that this question gets an answer? Thanks!2012-05-21

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