If P is a point of the ellipse x^ 2 a^ 2 + y^ 2 b^ 2 =1, whose foci are S and S’. Let ∠PSS’ = α and ∠PS’S= β, then

If P is a point of the ellipse x^ 2 a^ 2 + y^ 2 b^ 2 =1, whose foci are S and S’. Let…

Mathematics · JEE Advanced · NTA Exams — Co-ordinate Geometry

If P is a point of the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1,\)whose foci are S and S’. Let ∠PSS’ = α and ∠PS’S= β, then

PS + PS’ = 2a, if a > b
PS + PS’ = 2b, if a < b
\(\tan \frac{\alpha}{2} \tan \frac{\beta}{2}=\frac{1-e}{1+e}\)
\(\tan \frac{\alpha}{2} \tan \frac{\beta}{2}=\frac{\sqrt{a^{2}-b^{2}}}{b^{2}}\left[a-\sqrt{a^{2}-b^{2}}\right]\) when a > b

(A) PS + PS’ = 2a, if a > b, (B) PS + PS’ = 2b, if a < b, (C) 2 2 = 1-e 1+e

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