How to find radius of ellipse at any point $(x_1,y_1)$.
We know semi-major axis and semi-minor axis i.e. $a$ & $b$.
center of ellipse $(x_0,y_0)$.
Somewhere I found.
$$ r = \frac{ab}{\sqrt{ a^2 \sin^2\theta + b^2 \cos^2\theta}}$$
but here $θ$ is unknown?
Please help….
Best Answer
The $\theta$ represents the angle between the $x$-axis and the line which passes the center and $(x_1,y_1)$.
In other words, the $\theta$ satisfies $$\tan\theta=\frac{y_1}{x_1}$$ if $\theta\not=\frac{\pi}{2}.$
See this figure.