What is the eccentricity of a conic section? How can you classify conic sections by eccentricity? How does eccentricity change the shape of ellipses and hyperbolas?
Joni Kenny
Answered question
2020-11-09
Answer & Explanation
hosentak
Skilled2020-11-10Added 100 answers
Step 1 Any conic section may be described as the collection of points with constant ratios between their distances to the focus and directrix. The eccentricity of the conic section, sometimes abbreviated as e, is the name given to that ratio. Step 2 An ellipse that is not a circle has an eccentricity (e) that is larger than zero but less than 1. If then it is Parabola. If then comes a hyperbola [A hyperbola's eccentricity has no upper limit and can be any real value larger than 1. A rectangular hyperbola's eccentricity . If suddenly Circle appears. Step 3 An ellipse's eccentricity is almost zero if it is almost circular. An ellipse has a high degree of ovalness if its eccentricity is close to one. A conic section's eccentricity indicates how near it comes to having a circular form. The form resembles a circle less and less when the eccentricity of a conic section deviates from 0. A compressed circle resembles an ellipse. The closest analog to a circle among the other two conic forms is this one. A parabola would be the next closest shape to a circle, while a hyperbola would be the furthest, according to same reasoning.
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