# Exploration of the conjugate diameter of a hyperbola

- Author:
- Alison Middelkoop

- Topic:
- Hyperbola

**Investigating the notion of a conjugate diameter of a hyperbola:**A hyperbola is shown with a diameter passing through the centre C between points A and B. To quickly "draw" the following steps, click on the dot next to the object in the left hand menu to display it in the diagram. You will need to scroll down the list of objects. Segments are down at the bottom. 1. Draw

**line segments e and g**parallel to AB 2. Draw

**midpoints M1 and M2**of these two segments 3. Draw

**line h**through M1 and M2. You will see that this line also passes through the centre C. Although this line does not pass through the hyperbola it is considered the conjugate diameter to AB. 4. Draw

**line segments j and l**which are parallel to line h 5. Draw the

**midpoints M3 and M4**of these line segments 6. Draw

**line m**through M3 and M4. We are now back full circle to the original diameter line through A and B. NB. Points A and B can be moved by clicking and dragging. If you wish to change shape/position of hyperbola reveal Focus F1 of the hyperbola and click and drag.