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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