Consider an ellipse of the form $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$.
And draw a Chord that subtends $90°$at the centre of an ellipse.
This configuration has appeared in many of the ellipse questions.
I know only two of the properties. i.e
- $PQ$ is a variable chord of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ . If $PQ$ subtends right angle at the centre of ellipse then $\frac{1}{OP^2}+\frac{1}{OQ^2}= \frac{1}{a^2}+\frac{1}{b^2}$, where O is the center of the ellipse.
- The chord of contact of tangents drawn from the point $(h, k)$ to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ subtends a right angle at the centre, if
$$\frac{h^2}{a^4}+\frac{k^2}{b^4}=\frac{1}{a^2}+\frac{1}{b^2}$$
Can someone please tell me more about this configuration, and properties associated with this.