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I have a problem where I know the distance from one of the foci to the far side of the ellipse $(A+C)$ and I know $B$. How would I find out what $A$ and $C$ are separately?

EDIT: Sorry for the confusion. $A$ is the semi-major axis. $B$ is the semi-minor axis. And $C$ is the distance from the center to each focus.

So I know the distance from one focus to the far end, which would be $C$ (distance from focus to center) + $A$ (semi-major axis). But I don't know $C$ or $A$ individually.

Was trying to use the ellipse equation $C^2 = A^2-B^2$ but was unable to come up with a solution.

mls
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    Not sure what $A,B,C$ are in this context. Is $A$ the distance between the foci and $C$ the distance between the focus and the boundary? What is $B$? – gt6989b May 08 '19 at 18:27
  • For example $((a+c) =9 ,b=3 ) ,( a=? c=?) ? $ If that is the case, $ a^2 + \sqrt{a^2-b^2}=9 $ is a quadratic in $a$ to be solved. – Narasimham May 09 '19 at 04:09

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Assuming that $a$, $b$ and $c$ are the semi-major, semi-minor axes and linear eccentricity of the ellipse, respectively, the $a$ and $c$ can be computed from the equations: $$ a+c=r,\quad a^2-c^2=b^2, $$ where $r$ is the distance from one of the foci to the far side of the ellipse.

Substitution of either $a$ or $c$ from the first equation into the second one results in: $$a=\frac{r^2+b^2}{2r},\quad c=\frac{r^2-b^2}{2r}. $$

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