The eccentricity of a hyperbola | Conic sections | Geometry | 1

Описание: The eccentricity of a hyperbola is a number strictly greater than 1 that determines the shape of the hyperbola - that is, how wide or narrow the opening of the two branches of the hyperbola is. To calculate the eccentricity of a hyperbola, we divide the focal distance of the #hyperbola by its semi-transverse axis. In mathematical terms, e = c / a.

The focal distance is the distance from the centre to either focus, and the semi-transverse axis is the distance from the centre to either vertex. For a hyperbola to exist, the #focalDistance must always be strictly greater than the semi-transverse axis.

The closer the eccentricity is to 1, the narrower the opening of the two branches of the hyperbola becomes, and the closer the two foci are to the vertices. Conversely, the further the eccentricity is from 1, the wider the opening of the two branches becomes, and the farther the two foci are from the vertices. In other words, as the eccentricity approaches infinity, the two branches of the hyperbola increasingly resemble two #parallelLines.

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Timestamps

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00:17 e = 1.05
01:55 e = 1.1
02:14 e = 1.2
02:32 e = 1.3
02:50 e = 1.4
03:07 e = 1.5
03:24 e = 1.6
03:40 e = 1.7
03:56 e = 1.8
04:12 e = 1.9
04:28 e = 2
04:44 e = 2.5
04:59 e = 3
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#conicSections
#conics
#hyperbolas
#eccentricity #eccentric

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