Chord Through a Given Point

Chord Through a Given Point

For a chord joining points with eccentric angles $$\theta_1$$ and $$\theta_2$$ and passing through $$P(x_1,y_1)$$:

$$\frac{x_1\cos\left(\frac{\theta_1+\theta_2}{2}\right)}{a}+\frac{y_1\sin\left(\frac{\theta_1+\theta_2}{2}\right)}{b}=\cos\left(\frac{\theta_1-\theta_2}{2}\right)$$

Usage

- Used to establish the relation between the endpoint parameters of a chord passing through a known point.