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paintednails

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**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