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Kepler's law

  1. Nov 12, 2006 #1
    kepler's law!!

    hi, does anybody know how to prove that the eccentricity multiplied by the directrix is equal to [itex] \frac {b^2}{a} [\itex]?

    i found that the eccentricity of an ellipse is equal to c/a.

    i also found that the directrix is equal to a/e. the way i see it, if i multiply e and d, then i get

    ed = a

    but how do i prove that a = b^2 / a ?

    please help, thanks <3
  2. jcsd
  3. Nov 13, 2006 #2


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    ?? What do you mean by the directrix of an ellipse? A parabola has a directrix but it is a line, not a number.
  4. Nov 13, 2006 #3


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    I suspect we have an ellipse with center at the origin, major axis on the x-axis, minor on the y, foci at +/-c, major axis length a, minor length b, and vertical directrices at x=+/-a/e

    Ifa=b2/a, then a2=b2, which means you really have a circle.
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