# Conic Sections - Parabola

- Author:
- Tobias Teo

- Topic:
- Conic Sections, Parabola

This applet demonstrates the focus-directrix definition of a parabola, that is:
A

**parabola**is the locus of a point*P*in a plane such that the distance between*P*and the focus*F*is equal to the distance between*P*and the directrix. In other words, if*M*is the foot of the perpendicular from*P*to the directrix, then*PF* = *PM*.

__How to use the applet:__Click on the buttons in the top row to see the following parabolas:

- Focus (*y*^{2}= 4*ax**a*,0), directrix*x*= -*a*- Focus (0,*x*^{2}= 4*ay**a*), directrix*y*= -*a*

**Reset view**to return the value of

*a*to 1. Click and drag on the

**slider**to change the value of

**a**. Click and drag on the

**point**

*M*to see how the point

*P*moves to satisfy the condition

*PF*=

*PM*. Click on

**Animate**to move the point

*M*automatically. Click on

**Stop**to stop the animation. Click on

**Trace On**to trace out the locus of the point

*P*as you move the point

*M*. Click on

**Trace Off**to stop tracing. To remove the trace from the screen, click and drag the window slightly. After observing the locus of

*P*, click on the check box

**Show parabola**to see the parabola for the given focus and directrix.