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| Curve studied by de Longchamps in 1890, who named it. |
 |
Cartesian equation:  ,
or 
(b > 0).
Cartesian parametrization:  .
Rational cubic with isolated point (O). Polar equation: 
(written 
when a = b). |
Given a parabola (P) (here
with equation 
) and a line (D) perpendicular to the axis of
(P) (here, with equation x = a), the
associated mixed cubic is the locus of the point M on a variable
line (D) passing by O, cutting (P)
in P and cutting (D) in Q such
that 
.
In other words, the mixed cubic is the cissoid
of the parabola (P) and the straight line (D);
it is a special case of Zahradnik
cissoid.
The name mixed cubic comes from the fact that this curve
has a linear asymptote (
)
as well as a parabolic asymptote (
).
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© Robert FERRÉOL 2017