title: Plotting an hyperbola with matplotlib
body: <p>I need to plot an hyperbola of the type (y-a<em>x)(y-b</em>x)=-1 with matplotlib, I've tried to express y(x) but it gives an sqrt with impossible values. How can I assign to y the values to be plotted?
  The function i want to plot is<br>
  $$(y-\log(r^a 10^c))(y-\log(r^b10^d))=-1$$<br>
  which I "can" be rewritten as<br>
  $$y=1/2[log(r^(a+b)10^(c+d))\pm\sqrt{-4+\log^2(r^(a-b)10^(c-d))}]$$</p>