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A hyperbolic sector is a region of the Cartesian plane bounded by a hyperbola and two rays from the origin to it. For example, the two points (a, 1/a) and (b, 1/b) on the rectangular hyperbola xy = 1, or the corresponding region when this hyperbola is re-scaled and its orientation is altered by a rotation leaving the center at the origin, as with the unit hyperbola.
The sound of a shell being fired was received by several microphones, and the time of reception sent to a computing center to plot the location. These systems were used into World War II . The first hyperbolic radio navigation system was the World War II -era Gee , introduced by the Royal Air Force for use by RAF Bomber Command .
The linear eccentricity of an ellipse or hyperbola, denoted c (or sometimes f or e), is the distance between its center and either of its two foci. The eccentricity can be defined as the ratio of the linear eccentricity to the semimajor axis a : that is, e = c a {\displaystyle e={\frac {c}{a}}} (lacking a center, the linear eccentricity for ...
For example, at a place where escape speed is 11.2 km/s, the addition of 0.4 km/s yields a hyperbolic excess speed of 3.02 km/s. = This is an example of the Oberth effect. The converse is also true - a body does not need to be slowed by much compared to its hyperbolic excess speed (e.g. by atmospheric drag near periapsis) for velocity to fall ...
The following are also concurrent: (1) the circle that is centered at the hyperbola's center and that passes through the hyperbola's vertices; (2) either directrix; and (3) either of the asymptotes. [22] Since both the transverse axis and the conjugate axis are axes of symmetry, the symmetry group of a hyperbola is the Klein four-group.
Each hyperbola is defined by = / and = / (with =, =) in equation . Hyperbolic motion is the motion of an object with constant proper acceleration in special relativity . It is called hyperbolic motion because the equation describing the path of the object through spacetime is a hyperbola , as can be seen when graphed on a Minkowski diagram ...
x ℓ is the distance from the foot of the perpendicular to the x-axis to the origin (positive on one side and negative on the other, the same as in axial coordinates). [1] y ℓ is the distance along the perpendicular of the given point to its foot (positive on one side and negative on the other).
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