Given the length of the semi-major axis, and the distance between the 2 focus, how can I find the length of the semi-minor axis?
Might be difficult to get what I want to say but try to follow.Originally Posted by kidluff
The sum of any two distances from the focii to any point on the eilliple is the same (definition). Take the extreme point all the way on top where you put B.
Now the sum of the distances is,
$\displaystyle \sqrt{(s/2)^2+B^2}+\sqrt{(s/2)^2+B^2}$ where $\displaystyle s$ is distance between the focii.
Take the extreme point all the way on the semi-major axis where A is, and the sum of the distances is,
$\displaystyle (A-s/2)+(s/2+A)=2A$
Set them equal to each other,
$\displaystyle 2\sqrt{(s/2)^2+B^2}=2A$
Thus,
$\displaystyle (s/2)^2+B^2=A^2$
Thus,
$\displaystyle B=\sqrt{A^2-\frac{s^2}{4}}$