If the vertex of a hyperbola bisects the distance between its center and the correspoinding focus, then the ratio of the square of its conjugate axis to the square of its transverse axis is (a) 2 (b) 4 (c) 6 (d) 3

Options

A. 2
B. 4
C. 6
D. 3

Answer

C

Explanation

Let the hyperbola be
`(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`
Then, 2a = ae, i.e., e = 2. Therefore,
`(b^(2))/(a^(2))=e^(2)-1=3`
`"or "((2b)^(2))/((2a)^(2))=3`