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  2. Eccentricity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Eccentricity_(mathematics)

    The eccentricity can be defined as the ratio of the linear eccentricity to the semimajor axis a: that is, = (lacking a center, the linear eccentricity for parabolas is not defined). It is worth to note that a parabola can be treated as an ellipse or a hyperbola, but with one focal point at infinity .

  3. Hyperbolic trajectory - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_trajectory

    With eccentricity just over 1 the hyperbola is a sharp "v" shape. At e = 2 {\displaystyle e={\sqrt {2}}} the asymptotes are at right angles. With e > 2 {\displaystyle e>2} the asymptotes are more than 120° apart, and the periapsis distance is greater than the semi major axis.

  4. Hyperbola - Wikipedia

    en.wikipedia.org/wiki/Hyperbola

    Given the above general parametrization of the hyperbola in Cartesian coordinates, the eccentricity can be found using the formula in Conic section#Eccentricity in terms of coefficients. The center ( x c , y c ) {\displaystyle (x_{c},y_{c})} of the hyperbola may be determined from the formulae

  5. Unit hyperbola - Wikipedia

    en.wikipedia.org/wiki/Unit_hyperbola

    The unit hyperbola is blue, its conjugate is green, and the asymptotes are red. In geometry, the unit hyperbola is the set of points (x,y) in the Cartesian plane that satisfy the implicit equation = In the study of indefinite orthogonal groups, the unit hyperbola forms the basis for an alternative radial length

  6. Hyperbolic motion (relativity) - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_motion_(relativity)

    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 ...

  7. Hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_functions

    A ray through the unit hyperbola x 2 − y 2 = 1 at the point (cosh a, sinh a), where a is twice the area between the ray, the hyperbola, and the x-axis. For points on the hyperbola below the x-axis, the area is considered negative (see animated version with comparison with the trigonometric (circular) functions).

  8. Lambert's problem - Wikipedia

    en.wikipedia.org/wiki/Lambert's_problem

    The semi-major axis of this hyperbola is | | and the eccentricity is | |. This hyperbola is illustrated in figure 2. Relative the usual canonical coordinate system defined by the major and minor axis of the hyperbola its equation is

  9. Semi-major and semi-minor axes - Wikipedia

    en.wikipedia.org/wiki/Semi-major_and_semi-minor_axes

    where (h, k) is the center of the ellipse in Cartesian coordinates, in which an arbitrary point is given by (x, y).The semi-major axis is the mean value of the maximum and minimum distances and of the ellipse from a focus — that is, of the distances from a focus to the endpoints of the major axis

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