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Question

If e1 is the eccentricity of the ellipse x216+y225=1 and e2 is the eccentricity of the hyperbola passing through the foci of the ellipse and e1e2=1, then equation of the hyperbola is

A
x29y216=1
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B
x216y29=1
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C
x29y225=1
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D
x225y29=1
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Solution

The correct option is B x216y29=1
We have e1=11625=35
e1e2=1e2=53
Clearly y-axis is transverse axis of the ellipse.
Thus, coordinates of focii of the ellipse are (0,±be1) or (0,±3).
Let hyperbola is, y2b2x2a2=1..(1)
given hyperbola passes through foci of the ellipse
b2=9 and also a2=b2(e21)=9(25/91)=16
Therefore, required hyperbola is, x216y29=1
Hence, option 'A' is correct.

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