Mathematics

Problem

Let the major axis of a standard ellipse equals the transverse axis of a standard hyperbola and their director circles have radius equal to

2R

and

R

respectively. If

e_1

and

e_2

are the eccentricities of the ellipse and hyperbola, then the correct relation is a.

4e_1^2 - e_2^2 = 6

e_1^2 - 4e_2^2 = 2

4e_2^2 - e_1^2 = 6

e_2^2 - 4e_1^2 = 2