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- both are conic sections ( the intersection of a cone by a plane)
- both have two directrices
- both have two foci
- the ellipse is the locus of points so that sum of the distances to the foci is constant/the hyperbola is the locus of points so that difference of the distances to the foci is constant.
- In projective geometry they are equivalent. Hyperbolas are just ellipses that cross over infinity. (imagine watching a big giant ellipse that goes off in one direction past the horizon line and then reemerges from the horizon line behind you. It would look just like a hyperbola.)
- The hyperbola is an ellipse with an imaginary semi-minor axis (a negative quare root; hence the change in sign in the hyperbola's formula)
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What are the four kinds of parabolas?
Conic Sections are figures that can be formed by slicing a three dimensional right circular cone with a plane. There are different ways to do this, and each way yields a different figure. These figures can be represented on the graph as well as algebraically. The four conic sections are circles, ellipses, parabolas, and hyperbolas.
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