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:

• y² = 4ax - Focus (a,0), directrix x = -a
• x² = 4ay - Focus (0,a), directrix y = -a

Click on 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.