0

Given the following curve $$\alpha(t)=(4sin(t),t,-4cos(t))$$ I gotta show it's in a surface.

I know $$x^2(t)+y^{2}(t)+z^{2}(t)=16+t^{2}$$ but I'm not sure what can I do with it.

mvfs314
  • 2,017
  • 15
  • 19
  • There are many surfaces that contain this curve. e.g. $x^2 + z^2 - 16 = 0$ and $x\cos(y) + z\sin(y) = 0$. You need to be more specific about what sort of surfaces you are locking for. – achille hui Oct 16 '20 at 19:17
  • @achillehui my exercise just asks to show it's in a surface and then, to draw it. I thought about getting the cylinder made by 16+t^2 – mvfs314 Oct 16 '20 at 19:25

1 Answers1

2

It is a helix, clearly situated on the cylindrical surface with equation:

$$x^2+z^2=16$$

Jean Marie
  • 81,803