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.