# Exploring shapes of a hyperbola

- Author:
- Chris Woodward

- Topic:
- Hyperbola

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.