Two ellipses go through each others focal points. Prove that the focal points are the vertices of a parallelogram.
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Solution
![](https://mirangu.com/wp-content/uploads/2022/11/GyroscopeSolution.png)
It must be noted that there exists a non-parallelogram solution that also fits the conditions:
![](https://mirangu.com/wp-content/uploads/2022/11/GyroscopeSolution2.png)
Poem
![](https://mirangu.com/wp-content/uploads/2022/11/GyroscopeBella.jpg)