Hyperbola in a sentence

Coordinate systems Cartesian coordinates An east-west opening hyperbola centered at (h,k) has the equation : The major axis runs through the center of the hyperbola and intersects both arms of the hyperbola at the vertices (bend points) of the arms.

A hyperbola approaches its asymptotes arbitrarily closely as the distance from its center increases, but it never intersects them; however, a degenerate hyperbola consists only of its asymptotes.

Directrix and focus A hyperbola can be defined as the locus of points for which the ratio of the distances to one focus and to a line (called the directrix) is a constant e that is larger than 1. This constant is the eccentricity of the hyperbola.

Each branch of the hyperbola has two arms which become straighter (lower curvature) further out from the center of the hyperbola.

Hence, the conjugate hyperbola does not in general correspond to a 90° rotation of the original hyperbola; the two hyperbolas are generally different in shape.

Here A(s,t) denotes the area under the hyperbola between s and t. Formally, ln(a) may be defined as the area under the hyperbola 1/x.

If one forms a rectangle with vertices on the asymptotes and two sides that are tangent to the hyperbola, the sides tangent to the hyperbola are 2b in length while the sides that run parallel to the line between the foci (the major axis) are 2a in length.

If the center of inversion is chosen as the hyperbola's own center, the inverse curve is the lemniscate of Bernoulli ; the lemniscate is also the envelope of circles centered on a rectangular hyperbola and passing through the origin.

Receivers identified which hyperbola they were on and a position could be plotted at the intersection of the hyperbola from different patterns, usually by using the pair with the angle of cut closest to orthogonal as possible.

In November, iSpace tested its reusable Hyperbola 2 with a 50 second or so hop test.

The Hyperbola-1 was earlier slated for launch in April, then early June, before slipping for unannounced reasons.

A charged tachyon traveling in a vacuum therefore undergoes a constant proper time acceleration and, by necessity, its worldline forms a hyperbola in space-time.

A line g drawn from one focus may intersect this circle in two points M and N; perpendiculars to g drawn through these two points are tangent to the hyperbola.

A parabola is a conic section that is tangent to Ω, and a hyperbola is one that crosses Ω twice.

Archimedes had written The Quadrature of the Parabola in the third century BC, but a quadrature for the hyperbola eluded all efforts until Saint-Vincent published his results in 1647.

A simple way of producing a hyperboloid is to rotate a hyperbola about the axis of its foci or about its symmetry axis perpendicular to the first axis; these rotations produce hyperboloids of two and one sheet, respectively.

As : one has for any hyperbolic angle that the point : : satisfies the equation : which is the equation of a hyperbola relative its canonical coordinate system.

A third construction relies on the definition of the hyperbola as the reciprocation of a circle.

At most populated latitudes and at most times of the year, this conic section is a hyperbola.

Conic section analysis of the hyperbolic appearance of circles Figure 10: The hyperbola as a circle on the ground seen in perspective while gazing down slightly, showing the circle's (non-parallel) tangents as asymptotes.