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KÜLP QUARTIC

Curve studied by Külp in 1868.
Other name: Külp conchoid (because of its resemblance to the conchoid of Nicomedes).

 
Cartesian parametrization: 
Cartesian equation:  i.e. .
Rational quartic.

The Külp quartic is the hyperbolism of the circle with respect to its centre and a tangent (special case of Granville egg).

Here, the circle is the circle with diameter [OA] where A(0, a) and the line is y = a.

The Külp quartic is also the projection on the plane xOy of the biquadratic, intersection of the cylinder of revolution and of the hyperbolic paraboloid .


This curve must not be mistaken for the quartic with polar equation  and Cartesian equation  which is very similar to it:

Compare to the witch of Agnesi.
 
 
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© Robert FERRÉOL 2017