The following is a graph of the *cissoid
of Diocles*, named in honor of the Greek scholar who was the
first to construct the cissoid about 160 B.C.

The vertical line x = 1 is an asymptote line for the cissoid. A cissoid can be defined as follows:

Given circle O with diameter AB. Construct
line m perpendicular to secant AB at B. Draw line n through A
such that it intersects m. Call the intersection of n and m point
Q. Label the intersection of n and circle O as point P. *The
cissoid is the locus of points P on line n such that AP = CQ (shown
in blue in the graph above).*

**Click here for
a GSP 4.0 sketch to manipulate/investigate.**

A *strophoid *is an extension of the
cissoid. In the diagram below, we see a construction of a right
strophoid.

Line n is perpendicular to ray DO at D.
Line m represents all lines through O intersecting line n at Q.
** The spheroid (shown in blue) is the locus of points P such
that QD = QP.** Note that the curve to the left of line
n is a cissoid.

**Click here
for a GSP 4.0 sketch to manipulate.**

The strophoid below can be represented with the polar equation

Notice the asymptote line at x = -1.

The strophoids above are *right strophoids*
because lines m and n are perpendicular. What would happen if
m and n were not perpendicular? The result is an *oblique strophoid.
*(See an example below.)

(The diagonal blue line and the x-axis correspond to lines n and m of the construction of the right strophoid.)

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