Exploring Hyperbolas: Connecting Equations, Graphs, and Geometry
Instructional Prompts for Students
- Toggle between Horizontal and Vertical. What changes in the equation? What changes in the graph?
- Turn on Asymptotes. How do they predict the direction of the branches?
- Move the center (h,k). How do the asymptotes and the curve shift?
- Turn on Foci. Can you verify that the distance difference to the foci is constant?
- Compare a Rectangular hyperbola (a=b) to a general one. What makes it unique?
- Try a Rotated hyperbola. How does the angle t affect both the curve and its asymptotes?