Taxicab circles, ellipses, and hyperbolas

To explore Taxicab circles: Use the slider labeled a and either of the two points G or B. To explore Taxicab Ellipses: Use the points G and B close enough that when you use slider a they will over lap. To explore Taxicab Hyperbolas: Use points S and Z and move the point R on the line to the left of the applet. This is somewhat incomplete, you will notice that there are places where you can put the points S and Z so that the intersection of the two circles are not marked by points.