Let the major axis of a standard ellipse equals the transverse axis...

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Let the major axis of a standard ellipse equals the transverse axis of a standard hyperbola and their director circles have radius equal to \( 2 R \) and \( R \) respectively. If \( e_{1} \) and \( e_{2} \) are the
P eccentricities of the ellipse and hyperbola then the correct relation is:

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(a) \( 4 e_{1}^{2}-e_{2}^{2}=6 \)
(b) \( e_{1}^{2}-4 e_{2}^{2}=2 \)
(c) \( 4 e_{2}^{2}-e_{1}^{2}=6 \)
(d) \( 2 e_{1}^{3}-e_{2}^{2}=4 \)
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