Kepler's law

1. Nov 12, 2006

paintednails

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 ?

2. Nov 13, 2006

HallsofIvy

Staff Emeritus
?? What do you mean by the directrix of an ellipse? A parabola has a directrix but it is a line, not a number.

3. Nov 13, 2006

Office_Shredder

Staff Emeritus
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.