Plotting a metric space a>0, c>0; 4ac-b2>0

fabbi007

Metric given by (d) in the textbook on page 48 in the following url. How could we plot this function and characterize what the metric looks like for varying a, b, c. Start by plotting the case when d(x,0)=1, a=b=c=1. Vary a, b, and c individually. Show plots for each case and Characterize how the shape of the metric changes.


http://books.google.com/books?id=t3S...0space&f=false


My attempt:

The equation yields either a parabola or ellipse. Not sure where to start. A direction or hint would help. Thanks for your responses.