What conic section is a hyperbola derived from?
1 Answer
Jul 30, 2018
It is not derived from a conic section - it is a conic section.
Explanation:
Given a cone in three dimensional space, if we take a plane slice of it, then we can get any of the following curves where the plane and the cone intersect:
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Circle. This happens when the plane is perpendicular to the axis of the cone.
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Ellipse. This happens when the plane is tilted from the perpendicular but less than the angle of the cone.
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Parabola. This happens when the plane is at the same angle to the axis as the cone itself.
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Hyperbola. This happens when the plane is at a smaller angle to the axis than the cone itself.
There are various exceptions resulting in a single point, line or pair of lines, but otherwise, the above are the possible conic sections.
