Length of a Semi-Diameter in a Given Direction

Length of a Semi-Diameter in a Given Direction

For a line through the centre making angle $$\theta$$ with the $$x$$-axis:

$$r=\frac{ab}{\sqrt{b^2\cos^2\theta+a^2\sin^2\theta}}$$

Usage

- Used to determine the distance from the centre to the ellipse along a specified direction.