Question: I'm using TikZ to draw some conic-section graphs. There is a built-in
ellipse command (semiaxes as two arguments) and a rudimentary parabola command (with a vertical axis, but one can rotate), but to draw a hyperbola I had to
fake it with a spline and externally compute the control points. I don't want to plot a sequence of pixels, I'd prefer something parametric that can be easily modified. Is there a short-cut to draw a hyperbola just from the semiaxes and the centre location, within TikZ?

I'm not unhappy with spline approximations, they work fine for, say, cardioids, but is there some simpler way to get a hyperbola with TikZ?

Answer: 
Look at sections 19.5 and 19.6 in the `pgf` manual. You can plot curves given by simple parametric equations, such as

```
 \draw[scale=0.5,domain=-3.141:3.141,smooth,variable=\t] plot ({\t*sin(\t r)},{\t*cos(\t r)});

```

So if you van find parametric equations of your hyperbola, you should be able to plot it.
This should do the trick

```
\draw plot[variable=\t,samples=1000,domain=-35:35] ({sec(\t)},{tan(\t)});

```