If e = 2 1 and ∣ PS 1 S 2 = α , ∣ PS 2 S 1 = β , ∣ S 1 PS 2 = γ , then cot 2 α , cot 2 γ and cot 2 β are in

tan 2 α tan 2 β = 1 + e 1 − e = 3 1

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Mathematics - Ellipse Question with Solution | TestHub

MathematicsEllipseMiscellaneous/MixedMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

If 'P' is any point on the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ . $S_{1}$ and $S_{2}$ are foci of the ellipse.

If $e = \frac{1}{2}$ and $∣ PS_{1} S_{2} = α, ∣ PS_{2} S_{1} = β, ∣ S_{1} PS_{2} = γ$ , then $cot \frac{α}{2}, cot \frac{γ}{2}$ and $cot \frac{β}{2}$ are in

Options:

Answer:

. A

Solution:

$tan \frac{α}{2} tan \frac{β}{2} = \frac{1 - e}{1 + e} = \frac{1}{3}$

Stream:JEESubject:MathematicsTopic:EllipseSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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