What conic section is a hyperbola derived from?

1 Answer
Jul 30, 2018

Answer:

It is not derived from a conic section - it is a conic section.

Explanation:

Given a cone in three dimensional space, if we take a plane slice of it, then we can get any of the following curves where the plane and the cone intersect:

  • Circle. This happens when the plane is perpendicular to the axis of the cone.

  • Ellipse. This happens when the plane is tilted from the perpendicular but less than the angle of the cone.

  • Parabola. This happens when the plane is at the same angle to the axis as the cone itself.

  • Hyperbola. This happens when the plane is at a smaller angle to the axis than the cone itself.

There are various exceptions resulting in a single point, line or pair of lines, but otherwise, the above are the possible conic sections.