# The Trisectrix as the Locus of Points of Intersection

The Trisectrix as the Locus of Points of Intersection

A trisectrix (red) is the locus of the points of intersection (red point ) of a moving horizontal line (blue) and a rotating line (black).

P

L

M

Initially, the line lies along the line and the line lies along the line . The line rotates clockwise about the origin at 1 radian per time unit, and the line moves toward the axis at a constant rate of units per time unit, so that both lines reach the axis at the same time. The line meets the axis at an angle .

L

y=1

M

x=0

M

O

L

x

2/π

x

M

x

θ