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Question

If e1 and e2 are respectively theeccentricities of the ellipse x218+y24=1and the hyperbola x29y24=1,then therelation between e1 and e2 is


A

3e21+e22=2

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B

e21+2e2e=3

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C

2e21+e22=3

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D

e21+3e22=2

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Solution

The correct option is C

2e21+e22=3


The standard form of the ellipse is

x218+y24=1,where a2=18 and b2=4

So,the eccentricity is calculated in the following way:

b2=2(1e21)

4=18(1e21)

29=1221

e21=79

The standard form of the hyperbola is

x29+y24=1,where a2=9 and b2=4

So,the eccentricity is calculated in the following way:

b2=a2(e221)

4=9(e221)

49=e221

2e21+e22=2×79+139

=279=3


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