If `ea n de '` the eccentricities of a hyperbola and its conjugate, prove that `1/(e^2)+1/(e '^2)=1.`

Options

A. 0
B. 1
C. 2
D. 3

Answer

B

Explanation

Let the equation hyperbola and conjugate hyperbola be `(x^(2))/(a^(2))=1 and (x^(2))/(a^(2))=-1.`
then, the eccentricities are `e^(2)=(a^(2)+b^(2))/(a^(2))and e'^(2)=(a^(2)+b^(2))/(b^(2))`
`therefore (1)/e^(2)+(1)/(e'^(2))=a^(2)/(a^(2)+b^(2))+b^(2)/(a^(2)+b^(2))=1`