If two points 
and 
are inverse with respect to a circle
(the inversion circle), then the straight line
through 
which is perpendicular to the line of the points
is called the polar
of the point 
with respect to the circle, and
is called the pole of the polar.
An incidence-preserving transformation in which points and lines are transformed into their poles and polars is called a reciprocation.
The concept of poles and polars can also be generalized to arbitrary conic sections. If two tangents to a conic section
at points 
and 
meet at 
,
then 
is called the pole of the line 
with respect to the conic and 
is said to be the polar of the
point 
with respect to the conic (Wells 1991). Let a line through 
meet a conic at points 
and 
and its polar 
at 
. Then 
, 
,
, and 
are a harmonic range (Wells
1991). Furthermore, if two lines through a pole 
meet a conic at points 
and 
and points 
and 
, then the lines 
and 
meet on the polar, as do the lines 
and 
.
The concept can be generalized even further to an arbitrary algebraic curve so that every point has a polar with respect to the curve and every line has a pole (Wells 1991).
