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If the eccentricites of the ellipse x^(2...

If the eccentricites of the ellipse `x^(2)/4,y^(2)/3=1 and the hyperbola `x^(2)/64,y^(2)/b^(2)=1 are reciprocals of each other, then `b^(2)` is equal to

A

192

B

64

C

16

D

32

Text Solution

Verified by Experts

Q Eccentricity of ellipse `= sqrt(1- ( b^(2))/( a^(2))) = sqrt( 1-( 3)/( 4)) = ( 1)/(2)`
`:.` Eccentricity of hyperbola `= 2 rArr sqrt( 1+ (b^(2))/( 64)) rArr 4 = 1 +(b^(2))/( 64)rArr 192 = b^(2)`
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