Near branch of a hyperbola in polar coordinates with respect to a focal point

Description

In mathematics, a hyperbola is a type of smooth curve, lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows. Hyperbola is a conic section, formed by the intersection of a plane and a double cone and the plane intersects both halves of the double cone but does not pass through the apex of the cones. A hyperbola consists of two disconnected curves called its arms or branches. The distance from a point on the left branch of the hyperbola (in canonical form) to the left focal point has polar coordinates depending on the eccentricity of the hyperbola, the semi-major axis and the true anomaly of the point.

Related formulas

Variables

rThe distance from the point on the left branch of the hyperbola to the left focal point (m)
aSemi-major axis (m)
ϵThe eccentricity of the hyperbola (dimensionless)
θThe polar angle of the point on the hyperbola relative the near focal point ( true anomaly of the point) (radians)