6.3 Conic Sections - Hyperbola (copy)

A conic section defined as the set of all points on a plane where the absolute difference of their distances from fixed points is a constant.

A conic section defined as the set of all points on a plane where the absolute difference of their distances from fixed points is a constant.

Hyperbola

The line segment connecting the vertices of a hyperbola.

Transverse Axis

The line segment joining the points on a hyperbola that are equidistant from the center.

Conjugate Axis

The point of intersection of the transverse and conjugate axes of a hyperbola.

Center

The standard equation of a hyperbola, given by (x-h)^2/a^2 - (y-k)^2/b^2 = 1 for a horizontal principal axis and (y-k)^2/a^2 - (x-h)^2/b^2 = 1 for a vertical principal axis.

Hyperbola Equation

The points on a hyperbola that lie on the transverse axis.

Vertices

The fixed points inside a hyperbola that determine its shape.

Foci

The lines that a hyperbola approaches but never intersects.

Asymptotes

The lines that are equidistant from the foci and perpendicular to the transverse axis.

Directrices

A measure of how "stretched" or "flattened" a hyperbola is, given by the ratio of the distance between the center and a focus to the distance between the center and a vertex.

Eccentricity

A rectangle formed by the vertices and endpoints of the conjugate axis of a hyperbola.

Auxiliary Rectangle