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Q.

If the line joining the points A(α) and Bβ on the ellipse x225+y29=1 is a focal chord then one possible value of cotα2cotβ2 is

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a

–3

b

9

c

3

d

–9

answer is C.

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Detailed Solution

Given ellipse x225+y29=1

Equation of chord joining the points A(α) and B(β) is x5cosα+β2+y3sinα+β2=cosα-β2

since it is a focal chord then it passes through the focus (4,0)

45cosα+β2=cosα-β2

cosα+β2cosα-β2=54

Now cosα+β2+cosα-β2cosα+β2-α-β2=5+45-4

2cosα2cosβ2-2sinα2sinβ2=9 cotα2 cotβ2=-9

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