Please forgive my terminology if it is imprecise. In the diagram below, for known values of X, Y and Z, I am need to calculate the value (length) of M. (It's not homework, it's for an SVG animation...)
Thanks in advance.
Please forgive my terminology if it is imprecise. In the diagram below, for known values of X, Y and Z, I am need to calculate the value (length) of M. (It's not homework, it's for an SVG animation...)
Thanks in advance.
In the following I will take $X$ and $Y$ as the semiaxes of the ellipse. The equation of the ellipse is $ \frac{x^2}{X^2}+\frac{y^2}{Y^2}=1. $ You know $Z$, and you want to find $M$ sucha that the point $(M,Z)$ is on the ellipse. Substituting in the equation and a little algebra gives $ M=\frac{X}{Y}\sqrt{Y^2-Z^2}. $
HINT:
Ellipse equation is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
where $a$ is $X/2$ and $b$ is $Y/2$ according to your diagram.
Put $y=N$ in ellipse equation. $\frac{x^2}{a^2}+\frac{N^2}{b^2}=1$ and find two coordinate values of x. Then subtract them to find M.