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Question

If e and e are the eccentricities of the ellipse 5x2+9y2=45 and the hyperbola 5x24y2=45 respectively, then ee is equal to

A
9
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B
4
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C
5
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D
1
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Solution

The correct option is D 1
Given equation of ellipse is x29+y25=1

e=1b2a2

e=159

e=23

and equation of hyperbola is

x232+y2(454)2=1

e=1+b2a2=  1+4549=8136=32

Now

ee=23×32=1

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