Quartic plane curve

Quartic plane curve

A quartic plane curve is a plane curve of the fourth degree. It can be defined by a quartic equation:

:Ax^4+By^4+Cx^3y+Dx^2y^2+Exy^3+Fx^3+Gy^3+Hx^2y+Ixy^2+Jx^2+Ky^2+Lxy+Mx+Ny+P=0.

This equation has fifteen constants. However, it can be multiplied by any non-zero factor without changing the shape of the curve. Therefore, quartic curves form a space of dimension fourteen. It also follows that there is exactly one quartic curve that passes through a set of fourteen distinct points in general position.

A quartic curve can have a maximum of:
* Four connected components
* Twenty-eight bi-tangents
* Three ordinary double points

Examples

*Toric section
*Klein quartic

* The bean curve is a special case of the crooked egg curve
* A spiric section is a special case of a toric section


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