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Question

# If e1 and e2 are respectively theeccentricities of the ellipse x218+y24=1and the hyperbola x29âˆ’y24=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(1−e21) ⇒4=18(1−e21) ⇒29=1−221 ⇒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(e22−1) ⇒4=9(e22−1) ⇒49=e22−1 ∴2e21+e22=2×79+139 =279=3

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