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BULLET NOSE CURVE

Curve studied by Pieter Schoute in 1883. |

Cartesian equation:
(special case of Lamé curve), or
or also .
Cartesian parametrization: . Rational quartic. Area between the curve and the asymptotes: 4 ab. |

The bullet nose curve is the image of the hyperbola (here ) by a biaxial inversion (axes those of the hyperbola), defined by: ; geometrically, it is the locus of the intersection points between a tangent to the hyperbola and the axes.

Do not mistake for the kappa.

Opposite, the family of quartics with equation ,
which are no longer rational (in green for k < 0, in red for
and in blue for k > 1).
The bullet nose curve is obtained for k = 1 (limit
between the blue and red curves). |

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© Robert FERRÉOL 2017