Also known as a Gauche Conic, Space Conic, Twisted Conic, or Cubical Conic Section. A third-order Space Curve having up to three points in common with a plane and having three points in common with the plane at infinity. A skew cubic is determined by six points, with no four of them Coplanar. A line is met by up to four tangents to a skew cubic.

A line joining two points of a skew cubic (Real or conjugate imaginary) is called a Secant of the curve, and a line having one point in common with the curve is called a Semisecant or Transversal. Depending on the nature of the roots, the skew conic is classified as follows:

- 1. The three Roots are Real and distinct (Cubical Hyperbola).
- 2. One root is Real and the other two are Complex Conjugates (Cubical Ellipse).
- 3. Two of the Roots coincide (Cubical Parabolic Hyperbola).
- 4. All three Roots coincide (Cubical Parabola).

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1999-05-26