Skew Conic

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).

See also Conic Section, Cubical Ellipse, Cubical Hyperbola, Cubical Parabola, Cubical Parabolic Hyperbola