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?

http://i14.photobucket.com/albums/a3...uff/elipse.jpg

Printable View

- Apr 23rd 2006, 03:10 PMkidluffBasic Conics Help (elipse)
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?

http://i14.photobucket.com/albums/a3...uff/elipse.jpg - Apr 23rd 2006, 03:53 PMThePerfectHackerQuote:

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,

$\displaystyle B=\sqrt{A^2-\frac{s^2}{4}}$ - Apr 23rd 2006, 03:58 PMkidluff
Ohhh I see :x

Thanks alott @_@