# How can I plot the stereographic projection?

Stereographic Projection

I've read the link above but I actually want something a bit different. I have a equation

$$a\cos{\theta}\cos{\varphi}+b\cos{\theta}\sin{\varphi}+c\sin{\theta}=0$$

which represents the intersection of a plane and the unit sphere. For all its solutions $(\theta,\varphi)$, I want to plot $(\tan{\frac{\theta}{2}\cos{\varphi},\tan{\frac{\theta}{2}\sin{\varphi}}})$, which is a circle with radius $\tan{\frac{\theta}{2}}$, on a plane.

How can I do that? Thanks!

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Have you already tried anything (assuming this is about Mathematica, not math in general)? –  Yves Klett Nov 4 at 7:46
You can adapt the linked question, if you calculate the inverse of the projection f in that question. Since $\theta$ depends on $\phi$, I don't think $\tan(\theta/2)$ represents the radius. –  Michael E2 Nov 4 at 11:48
@YvesKlett I'm not quite familiar with familiar with Mathematica, so all I can think of is to ContourPlot the first equation. But it's not anywhere near my goal xD –  Alex Su Nov 5 at 15:31