Generating Conics by Newton's Method

angle α

angle β

labels

show conic

move P

This Demonstration shows a construction of conics (parabola, ellipse, and hyperbola) attributed to Newton. Consider point P, constrained to move on a bar, joined to fixed points A and B by two lines and lines through A and B inclined at fixed angles

α

and

β

with these lines. Their intersection point will be on a conic as you move P.