Well, first, you need to write down the equation for the hyperbola. Seems silly, or maybe obvious, but you can't do anything without an equation. And we cannot tell you what the equation of a hyperbola is, when we are not given the equation. The mind reading toolbox is just too buggy still.
Then it is simplest to just use fimplicit. For example...
fun = @(x,y) x.^2 - y.^2 + x.*y + 2
You could as easily have used fimplicit to plot the ellipses too, but who cares what vehicle you use to get where you need to go?