 
bicircular quartic


last updated: 20041204 
The bicircular quartic is a bicircular
algebraic curve that is a quartic.
The curve is the cyclic of a conic.
When the conic has the Cartesian equation x^{2} / l + y^{2}
/ m^{ }= 1, the fixed point is (n, o), and the power of inversion is p,
then l, m, n, o and p can be written as function of a, b, c, d and e ^{1)}.
p=0
When the power of inversion (p) is equal zero, the curve is called rational: a bicircular
rational quartic.
This curve is the pedal of the circle
with respect to one of its points.
We know the following species:
p<>0
For p <> 0, the the following curves can be distinguished:
The bicircular quartic can also be written in a tripolar equation:
f r_{1} + g r_{2} + h r_{3} = 0.
notes
1) As follows:
a =  2 (2l+n^{2}+o^{2}p)
b =  2 (2m+n^{2}+o^{2}p)
c = 4ln
d = 4mo
e = (n^{2}+o^{2}p)^{2}  4 (ln^{2}+mo^{2})
