The bifolium is a quartic plane curve of the equation:

So, for example, a non-singular quartic plane curve is of genus 3 and has 28 bitangents and 24 points of inflection.

In mathematics, a Lüroth quartic is a nonsingular quartic plane curve containing the 10 vertices of a complete pentalateral.

In real algebraic geometry, a general quartic plane curve has 28 bitangent lines, lines that are tangent to the curve in two places.

The anticanonical divisor is not very ample, and its linear system defines a map from the del Pezzo surface to the projective plane, branched over a quartic plane curve.

Second, the union of two circles is a special (reducible) case of a quartic plane curve, and the external and internal tangent lines are the bitangents to this quartic curve.

A Cassini oval is a quartic plane curve defined as the set (or locus) of points in the plane such that the product of the distances to two fixed points is constant.