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Question

If the chord joining the points α and β on the ellipse x2a2+y2b2=1 subtends a right angle at (a, 0), then tan(α2)tan(β2)=


A
 
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B
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C
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D
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Solution

The correct option is C
P(acosα,bsinα),Q=(acosβ,bsinβ),R=(a,0)
Since PR⊥QR then bsinαa(cosα1).bsinβa(cosβ1)=1b2a2.cotα2.cotβ2=1tanα2tanβ2=b2a2

Mathematics

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