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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

The correct Answer is:
A
`because " Eccentricity of ellipse "=sqrt(1-(b^(2))/(a^(2)))=sqrt(1-(3)/(4))=(1)/(2)`
`therefore" Eccentricity of hyperbola "=2" "rArr" "sqrt(1+(b^(2))/(64))rArr 2" "rArr" "4=1+(b^(2))/(64)rArr 192=b^(2)`
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