Families of Conics

This construction allows you to graph the conics family defined by . The values of the four parameters are controlled by sliders on the left of the screen.
With which of the four parameters can you change the center of the conic? Which of the four parameters determine the conic that is graphed? Experiment with the sliders to determine the specific parameter conditions that guarantee hyperbolas. Under what parameter conditions will the equation yield circles, ellipses, or parabolas?