## Lesson 6-1: Parabolas

Imagine two red threads (segments), of equal length, which are connected at point P.

One goes to the point F (focus) and another continues to point D (directrix).

Manuel Sada and modified by Steven Lapinski, April 2005, Created with GeoGebra

## Objective:

The student will be able to define a parabola, graph a parabola, locate its vertex, directrix, focus and axis of symmetry.

Move Point D and observe trace of point P.

What kind of curve describes the trace P?

What can be said of the segments PF and PD?

What property meet all the points by passing P?

Click on the blue arrows to reset the applet.

You can move line a and points E and F to change the size of trace.

What happens to the trace when line a is moved?

- Click the Play Button under the movie.

- The red dot is always the center of the yellow circle.

- Which line(s) represent the radius of the circle?

- Which segments are always the same length?

- The trail of red dots forms a parabola - what distances must be equal to form a parabola?

**Livemath:** An interactive website that explains the parts of a parabola. Livemath