Exploring shapes of a hyperbola
- Chris Woodward
This applet allows you to explore how the defining elements of a hyperbola influence its shape. A hyperbola with focal points A and B and its asymptotes are shown. You can drag the foci and you can use the "diff" slider to change the focal difference (the difference of distances between a point on the hyperbola and the foci). Use the applet to answer the questions below.
Let's denote the focal distance by f and the distance between the foci by d. 1. For what kind of values of f and d does the hyperbola resemble a segment? 2. For what kind of values of f and d does the hyperbola resemble two parallel lines? 3. What kind of values of f and d make the hyperbola branches a) narrow; b) wide open? 4. Is there any situation in which the hyperbola turns into an ellipse? If yes, try to characterize for what values of d and f this happens and look for a theoretical explanation of why this is the case.