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Q.

 Let e1 and e2 be the eccentricities of the ellipse, x225+y2b2=1(b<5) and the hyperbola, x216-y2b2=1 respectively 

 satisfying e1e2=1 . If α and β are the distances between the foci of the ellipse and the foci of the 

 hyperbola respectively , then the ordered pair (α,β) is equal to 

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a

245,10

b

(8,12)

c

203,12

d

(8,10)

answer is A.

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Detailed Solution

e1=25-b225,e2=16-b216e1e2=1e1e22=125-b22516+b216=1 It gives b2=9

The distance between the foci: 

α=2a2b2=2259=8β=2a2+b2=216+9=10

 Therefore, (α,β)=(8,10)

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