TITLE: Number of normals to a parabola from a given point
QUESTION [6 upvotes]: 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

REPLY [10 votes]: 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.