# Strophoids

- Author:
- Steve Phelps

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 thatP'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.