Locus of Parabola
In the figure, F is the focus, L is the directrix, A is a moving point on L. Draw the perpendicular bisector of AF. Draw a perpendicular line from A. The above two lines intersect at P. By using the properties of congruent triangles, it can be shown that PF = PA. Hence the locus of P is a parabola. You may drag the point A to observe the locus of P.