Question

what is eccentricity​

Answer 1

Eccentricity of a conic section is the ratio of the distance of a point, on it, from the focus of it, to that from the directrix of it.

Answer 2

Answer:

In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape.

More formally two conic sections are similar if and only if they have the same eccentricity.

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 zero.

The eccentricity of an ellipse which is not a circle is greater than zero but less than 1.

The eccentricity of a parabola is 1.

The eccentricity of a hyperbola is greater than 1.

Any conic section can be defined as the locus of points whose distances to a point (the focus) and a line (the directrix) are in a constant ratio. That ratio is called the eccentricity, commonly denoted as e.

The eccentricity can also be defined in terms of the intersection of a plane and a double-napped cone associated with the conic section. If the cone is oriented with its axis vertical, the eccentricity is

e=sinβ/sinα, 0<α<90∘, 0≤β≤90∘ ,e=sin⁡βsin⁡α, 0<α<90∘, 0≤β≤90∘ ,

where β is the angle between the plane and the horizontal and α is the angle between the cone's slant generator and the horizontal. For β=0β=0 the plane section is a circle, for β=αβ=αa parabola. (The plane must not meet the vertex of the cone.)

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=cae=ca (lacking a center, the linear eccentricity for parabolas is not defined).

Adapted from Wikipedia…

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