A parabola is the set of points equidistant from a given point, called the [b]focus[/b], and a given line called the [b]directrix[/b]. In the diagram below, F is the focus and AB is the directrix. [br]C is any point on the directrix.

You can play around with A, B, F and C.[br][br]Given C and F, how do we find the point P on the parabola equidistant from C and F?[br]Hint: consider the right-angled triangle FGP; from this you may find the radius, |FP|.[br][br]If Q is the other point of intersection of the two circles, why does it lie on the axis, DF, of the parabola?[br][br]What do you notice about the line PQ?[br][br]Can you convince first a friend and then a sceptic about your answers to these questions?