✖

Cones

Kapitoly: Cones, Ellipse, Hyperbola, Parabola, Euclid's theorems

A conic line is a curve that results from the intersection of a plane with the shell of a rotating cone. The simplest such curve is a circle. Other conics are the ellipse, the parabola, and the hyperbola.

How conics are formed

The formation of conics is nicely illustrated in the following figure, which is borrowed from Wikipedia:

From left: parabola, ellipse and hyperbola

In the beginning we have an ordinary cone. We then intersect this cone with a plane that intersects the cone in various ways, and this intersection creates a new curve. We always consider only the shell of the cone, i.e. we really only get the curve - the inside of the cone is neglected.

Types of cones

  • Anellipse is a curve whose every point has the same sum of distances from a given two points in the plane.
  • Ahyperbola is a conic whose every point is such that the absolute value of the difference of distances from two fixed points is always the same.
  • A parabola is a curve that has a constant distance from a given line and from a given point not on that line.

Other resources