# Strophoids

Let S be any curve and O a point (called the pole) and a fixed point A. If a variable line through O meets curve S at Q, and points P and P' are on this line such that

P'Q = QP = QA

the locus of P and P' is called the strophoid of S with respect to the pole O and the fixed point A.

## Oblique Strophoid

A strophoid of a line with respect to a pole not on the line and a fixed point on the line.

## Right Strophoid

A strophoid of a line with respect to a pole not on the line where the fixed point is the foot of the perpendicular dropped from the pole.

## Freeth's Nephroid

The strophoid of a circle with respect to its center as the pole and a fixed point on the circumference.

## Other Strophoids

The strophoid of a circle with respect to a point on the circumference, with the fixed point being diametrically opposed to the pole.
The strophoid of a circle with its center as the pole and a fixed point not on the circle.
The strophoid of a parabola with the pole being the vertex and the focus being the fixed point.