If the eccentricities 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)=`

Options

A. 192
B. 64
C. 16
D. 32

Answer

A

Explanation

`therefore` eccentricity of hyperbola = `sqrt(1-b^(2)/a^(2)=)sqrt(1-(3)/(4)=(1)/(2)`
` therefore` eccentricity of hyperbola =2 `
`rArr sqrt(1+b^(2)/(64)=2`
`rArr 4=1+b^(2)/(64)rArr192=b^(2)`