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Question

If e1 is the eccentricity of the conic 9x2+4y2=36 and e2 is the eccentricity of the conic 9x24y2=36,then


A

e21e22=2

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B

2<e22e21<3

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C

e22e21=2

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D

e22e21>3

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Solution

The correct option is B

2<e22e21<3


The conic 9x24y2=36 can rewritten in the following way.

9x236+4y236=1

x24+y29=1

This is the standard equation of an ellipse.

b2=a2(1e1)2

9=4(1e1)2

(e1)2=54

The conic 9x24y2=36 can rewritten in the following way:

9x2364y29=1

x24y29=1

This is standard equation of a hyperbola

b2=a2(e221)

9=4(e221)

(e2)2=134

e22=134+54=2.5


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