## Christmas tree light

Forgive the sloppy use of math and inability to produce an image. I noticed this last christmas.

If you have a fairy light ( or perhaps any LED etc), and shine it normal to a surface, you see a circle. If you place the light flat on the surface you see a curve - to me the fairy lights' curve looks like a hyperbola.

Does this have any relation to the equation of a circle:
$$x^2+y^2=const.$$
And Hyperbola:
$$x^2-y^2=const.$$
And subsitution for 90 degrees rotation? :
$$y\rightarrow iy$$

If so, how does this even work? The experiment is all in real space. If not, is this just sloppy use of math? Any significance?

Thanks

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 Blog Entries: 27 Recognitions: Gold Member Homework Help Science Advisor Hi Livethefire! If the light comes out in a cone, then the shape will be the intersection of a cone with a plane … in other words, a conic section
 Ah yes! But is there any relevance or justified motivation to present such a thing by substituting "iy" in a circular equation?

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