[size=150][color=#3d85c6]The normal form(named after German mathematician Ludwig Otto Hesse) of equation of a straight line is as follows:[/color][math]\text{x}\cos\omega+y\sin\omega=p[/math][color=#3d85c6] where [/color][math]p[/math][color=#3d85c6] is the length of the perpendicular drawn from the origin onto the line and [/color][math]\omega[/math][color=#3d85c6] is the angle the normal makes with positive x-axis.[br][/color][/size]In the applet shown below OC is the perpendicular.So [math]OC=p[/math].You can drag points A and B on the line to different positions to change p and [math]\omega[/math].

Why was Hesse bent upon describing the equation in terms of the normal ? Put another way, why should we try to know [math]p[/math] and [math]\omega[/math] ?