For a unit circle with parametric equations
 |  |  |
(1)
|
 |  |  |
(2)
|
the negative pedal curve with respect to the pedal point 
is
 |  |  |
(3)
|
 |  |  |
(4)
|
Therefore if the point is inside the circle (
), the negative pedal is an ellipse,
if 
,
it is a single point, if the point is outside the circle (
), the negative pedal is a hyperbola.
