Equation for getting the length of the minor axis (of an ellipse) I'm looking for an equation that can help me determine the length of the minor axis.
I know the length of the major axis and have the Cartesian coordinates of a point somewhere on the ellipse. 
How can I use these to get the length of the minor axis?
 A: Added: In a comment OP  states that "The major axis is on the y-axis and the minor axis is on the x-axis."

The equation of an ellipse whose major and minor axis are respectively on
the $y$ and $x$-axis is
$$\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1,\qquad (\ast )$$
where $a$ is the semimajor axe and $b$ is the semiminor axe. You are given $%
2a$ and you need to find $2b$. Let the coordinates of the given point be $%
(x_{1},y_{1})$. Since it is on the ellipse, its coordinates must satisfy $%
(\ast )$
$$\frac{x_{1}^{2}}{b^{2}}+\frac{y_{1}^{2}}{a^{2}}=1.\qquad (\ast \ast )$$
Clearing denominators and then dividing by $y_{1}^{2}-a^{2}$ we get
$$a^{2}x_{1}^{2}+b^{2}y_{1}^{2}=a^{2}b^{2}\Leftrightarrow \left(
y_{1}^{2}-a^{2}\right) b^{2}=-a^{2}x_{1}^{2}\Leftrightarrow b^{2}=-\frac{%
a^{2}x_{1}^{2}}{y_{1}^{2}-a^{2}}=\frac{a^{2}x_{1}^{2}}{a^{2}-y_{1}^{2}}.$$ 
Since $a^{2}-y_{1}^{2}\geq 0$ and $b>0$, we obtain
$$b=\frac{a|x_{1}|}{\sqrt{a^{2}-y_{1}^{2}}}.\qquad (\ast \ast \ast )$$
The length of the minor axe is $2b$.
A: So you know the length of the semimajor axis, and it's along y. Let's call this axis 'a'. We'll call the length of the semiminor axis 'b'.
x^2 / b^2 + y^2 / a^2 = 1.
You also have another point (x1, y1).
Simply sub this into the equation and solve for b!
x1^2 / b^2 + y1^2 / a^2   = 1
(a^2 - y^1)/ a^2          = x1^2 / b^2
x1^2 * a^2 / (a^2 - y1^2)`= b^2

Of course, this approach won't work if a^2 = y1^2 (as you'll be dividing by 0), but a point on the ellipse should mean this will never be the case.
I may have made an algebraic mistake somewhere there, but the approach should still be good. :)
Hope this helps.
