Sum of Reciprocal Focal Distances

Rarely Tested

Sum of Reciprocal Focal Distances

For any point $$p$$ on the ellipse:

$$PS_1+PS_2=2a$$

and therefore:

$$\frac{1}{PS_1}+\frac{1}{PS_2}=\frac{2a}{PS_1PS_2}$$

Usage

- Used in problems involving reciprocal focal distances.

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