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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 .
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
where e is the eccentricity and l is the semi-latus rectum. As above, for e = 0, the graph is a circle, for 0 < e < 1 the graph is an ellipse, for e = 1 a parabola, and for e > 1 a hyperbola. The polar form of the equation of a conic is often used in dynamics; for instance, determining the orbits of objects revolving about the Sun. [20]
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.
The length of the semi-minor axis could also be found using the following formula ... in the equation of the hyperbola relative ... eccentricity e = 0.0549, its semi ...
The equation for a conic section with apex at the origin and tangent to the y axis is + (+) = alternately = + (+) where R is the radius of curvature at x = 0. This formulation is used in geometric optics to specify oblate elliptical ( K > 0 ), spherical ( K = 0 ), prolate elliptical ( 0 > K > −1 ), parabolic ( K = −1 ), and hyperbolic ( K ...
When 0 < a < c the conic is a hyperbola; when c < a the conic is an ellipse. Each ellipse or hyperbola in the pencil is the locus of points satisfying the equation + = with semi-major axis as parameter.
The mean eccentricity of an object is the average eccentricity as a result of perturbations over a given time period. Neptune currently has an instant (current epoch ) eccentricity of 0.011 3 , [ 11 ] but from 1800 to 2050 has a mean eccentricity of 0.008 59 .