Equation of Chord Joining Two Parametric Points

Equation of Chord Joining Two Parametric Points

For the ellipse:

$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$

the chord joining the points corresponding to parameters $$\theta_1$$ and $$\theta_2$$ is:

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

Usage

- Used to obtain the equation of a chord when the parameters of its endpoints are known.

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