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In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular: The eccentricity of a circle is 0. The eccentricity of an ellipse which is not a circle is between 0 and 1.
Conic sections of varying eccentricity sharing a focus point and directrix line, including an ellipse (red, e = 1/2), a parabola (green, e = 1), and a hyperbola (blue, e = 2). The conic of eccentricity 0 in this figure is an infinitesimal circle centered at the focus, and the conic of eccentricity ∞ is an infinitesimally separated pair of lines.
In geometry, the conic constant (or Schwarzschild constant, [1] after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the letter K. The constant is given by K = − e 2 , {\displaystyle K=-e^{2},} where e is the eccentricity of the conic section.
The eccentricity of the conic section obtained by reciprocation is the ratio of the distances between the two circles' centers to the radius r of reciprocation circle C. If B and C represent the points at the centers of the corresponding circles, then = ¯.
Unwrap the cone to a plane. Then the curve in the plane to which the conic section of eccentricity λ is unwrapped is a generalized conic with polar equation as specified in the definition. In the special case when k < 1, the generalized conic cannot be obtained by unwrapping a conic section. In this case there is another interpretation.
A conic is defined as the locus of points for each of which the distance to the focus divided by the distance to the directrix is a fixed positive constant, called the eccentricity e. If 0 < e < 1 the conic is an ellipse, if e = 1 the conic is a parabola, and if e > 1 the conic is a hyperbola.
The solution of this equation is = [+ ()] which shows that the orbit is a conic section of eccentricity e; here, φ 0 is the initial angle, and the center of force is at the focus of the conic section.
Pages in category "Conic sections" The following 51 pages are in this category, out of 51 total. ... Eccentricity (mathematics) Eleven-point conic; Ellipse; Ellipsograph;