Number of normals to a parabola from a given point I know that from any point a maximum of three normals could be drawn to a parabola because the equation of normal is cubic. 
But I want to know the condition on the point for the number of normals
Claude's technique can be extended slightly to find the the points and normal lines given a particular point off of the parabola. Using this, I obtained an animation of some of the normals.
Only two perpendicular tangents can be drawn from a point P on a parabola directrix ( standard result, need not be again proved). Taking this as given we complete the rectangle by drawing parallels to arrive at a unique opposite point inside point Q ... from which we conclude accordingly only 2 unique normals can be drawn from an arbitrary but inside point like Q.