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P is any point lying on the ellipse (x^(...

P is any point lying on the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1(agtb)` whose foci are S and S'. If `anglePSS'=alpha and anglePS'S=beta`, then the value of `tan.(alpha)/(2)tan.(beta)/(2)` is

A

`(1+e)/(1-e)`

B

`(1+e^(2))/(1-e^(2))`

C

`(1-e)/(1+e)`

D

1

Text Solution

AI Generated Solution

To solve the problem, we need to find the value of \(\frac{\tan(\alpha/2)}{\tan(\beta/2)}\) where \(P\) is a point on the ellipse given by the equation \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) with \(a > b\). The foci of the ellipse are denoted as \(S\) and \(S'\). ### Step-by-Step Solution: 1. **Understanding the Ellipse and Foci**: The foci \(S\) and \(S'\) of the ellipse are located at \((\pm ae, 0)\), where \(e = \sqrt{1 - \frac{b^2}{a^2}}\). 2. **Identifying Angles**: ...
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