Move the various sliders in this applet around to investigate what happens to the graph of a hyperbola as you change various parameters within the standard form of its equation. Checkboxes are provided for you to select whether you want the hyperbola to have a horizontal transverse axis vs. a vertical transverse axis.
Key questions:
Is it possible to tell the location of a hyperbola's center just by looking at its equation? If so, how?
How can the length of an hyperbola's transverse axis & conjugate axis be determined just by looking at its equation?
What are the key differences in the standard form of the equation of a hyperbola with a horizontal transverse axis vs. a vertical transverse axis?