Endpoints of the Conjugate Diameter

Endpoints of the Conjugate Diameter

If one diameter has endpoints:

$$P(a\cos\theta,b\sin\theta),\quad P'(-a\cos\theta,-b\sin\theta)$$

then the endpoints of its conjugate diameter are:

$$Q(-a\sin\theta,b\cos\theta),\quad Q'(a\sin\theta,-b\cos\theta)$$

Usage

- Used to construct the conjugate diameter from a known diameter.