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I wasn't sure if this is a Computational Science SE question or a Stack Overflow question but I think it's more of this one.

I wanted to make a graph where I can rotate a hyperbola (not parabola or ellipse) about any point, not just the origin on a Cartesian Plane. This is the equation: $$\left(\frac{(y-k)\sin\theta-(x-h)\cos\theta}a\right)^2-\left(\frac{(y-k)\cos\theta-(x-h)\sin\theta}b\right)^2=1$$

But when I plot this equation in Desmos, it keeps saying Too many variables. I don't know what to do with this. It seems like the $\sin$ and $\cos$ are causing it to say that because when I take it out, it doesn't say that anymore.

Question: Why is it saying that? How is the $\sin$ and $\cos$ causing it to say there are too many variables. Is my equation wrong or is it the graphing calculator itself that is at fault?

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  • $\begingroup$ In your equation, what are the actual variables and what are parameters out of $x,y,a,k,b,h,\theta$? $\endgroup$ – Anton Menshov♦ Apr 2 '20 at 20:22
  • $\begingroup$ @AntonMenshov a is the distance of the vertex to the origin, b is the distance from the vertex to the asymptote, h and k are the points of rotation, and theta is the angle of rotation. $\endgroup$ – Star Man Apr 2 '20 at 20:30
  • $\begingroup$ In general, these types of questions are off-topic here. However, they also can be totally lost on SO and not receive any attention. $\endgroup$ – Anton Menshov♦ Apr 2 '20 at 20:36
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Desmos seems to be picky about variable names. The moment I renamed $\theta$ into $t$, the plotting started to work correctly.

Desmos plot link

enter image description here enter image description here

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  • $\begingroup$ Wow. Thank you very much, sir. I was so fed up as to why it wasn't working while all I had to do was just rename $\theta$. Thanks. $\endgroup$ – Star Man Apr 2 '20 at 20:38

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