Given point F (=focus), and line [math]\ell[/math] (=directrix).[br]Q is a point equidistant from the point and the line.[br]Try moving Q

Let [math]F=\left(\frac{p}{2},0\right)[/math], and [math]\ell:x=-\frac{p}{2}[/math].[br]How does changing the parameter [math]p[/math] affect the parabola?

And how about other points in the plane? [br][br]In the applet below, move around point P, and try to notice:[br]which points are closer to the focus, and which to the directrix?