Let [i]S[/i] be any curve and [i]O[/i] a point (called the pole) and a fixed point [i]A[/i]. If a variable line through [i]O[/i] meets curve [i]S [/i]at [i]Q[/i], and points [i]P[/i] and [i]P[/i]' are on this line such that [br][br][i][center]P'Q = QP = QA[/center][/i]the locus of [i]P[/i] and [i]P[/i]' is called the [i][b]strophoid of S with respect to the pole O and the fixed point A[/b][/i].

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

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.

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

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.