Prove that the geometric mean between the greatest linear speed of movement along an ellipse with a semi-major axis o and

Prove that the geometric mean between the greatest linear speed of movement along an ellipse with a semi-major axis o and the smallest is equal to the speed of movement in a circle of radius a. At what point in the orbit does the body have such a speed?

The speed at the ends of the minor axis is equal to the average speed.

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