Bullet-nose curve

Plane curve of the form a²y² – b²x² = x²y² From Wikipedia, the free encyclopedia

Bullet-nose curve

In mathematics, a bullet-nose curve is a unicursal quartic curve with three inflection points, given by the equation

Thumb
Bullet-nose curve with a = 1 and b = 1

The bullet curve has three double points in the real projective plane, at x = 0 and y = 0, x = 0 and z = 0, and y = 0 and z = 0, and is therefore a unicursal (rational) curve of genus zero.

If

then

are the two branches of the bullet curve at the origin.

References

  • J. Dennis Lawrence (1972). A catalog of special plane curves. Dover Publications. pp. 128–130. ISBN 0-486-60288-5.
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