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[parent] confocal (Definition)

Two conics are confocal if they have coincident foci.

Examples

  1. The family of ellipses
    $\displaystyle \frac{x^2}{a^2+s}+\frac{y^2}{b^2+s} = 1,$
    where $ a^2 > b^2$ and the parameter $ s$ is $ > -b^2$, is confocal.
  2. The family of hyperbolas
    $\displaystyle \frac{x^2}{a^2-t}-\frac{y^2}{t-b^2} = 1,$
    where $ a^2 > b^2$ and the parameter $ t$ is between $ a^2$ and $ b^2$, is confocal.



"confocal" is owned by Mathprof. [ full author list (2) | owner history (1) ]
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hyperbolas orthogonal to ellipses (Example) by pahio
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Cross-references: hyperbolas, parameter, ellipses, foci, conics
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This is version 3 of confocal, born on 2004-10-17, modified 2007-04-09.
Object id is 6388, canonical name is Confocal.
Accessed 1459 times total.

Classification:
AMS MSC: 51N20 (Geometry :: Analytic and descriptive geometry :: Euclidean analytic geometry)
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