Move the center to re-position the hyperbola. Observe how the equation changes. Move the sliders to change the positions of the foci and vertices. Notice how this effects the length of the conjugate axis and the slopes of the asymptotes. Observe how the eccentricity changes as you change the values of "a" and "c". Trace the hyperbola to see how the difference in the distances to the foci from any point on the hyperbola is constant, and equals the length of the transverse axis.