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If PSQ + PHR be two chords of an ellipse...

If PSQ + PHR be two chords of an ellipse through its foci S and H, then prove that `(PS)/(SQ) + (PH)/(HQ) = 2(1 + e^2)/(1-e^2)`, Where e is the eccentricity of ellipse.

Text Solution

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We can draw an ellipse with the given details.
Please refer to video for the figure.
Equation of ellipse with respect to focus `S` as a pole,
`l/r = 1+ecos theta`
Here, `r = SP`,
`:. l/(SP) = 1+ e cos theta ->(1)`
If vectorial angle of `P` is `theta`, then vectorial angle of `Q` will be `pi+theta`.
If we write equation with respect to `SQ`, then,
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