If a variable line has its intercepts on the coordinate axis \( e \) and \( e^{\prime} \) where ...

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If a variable line has its intercepts on the coordinate axis \( e \) and \( e^{\prime} \) where \( \frac{\mathrm{e}}{2} \) and \( \frac{e^{\prime}}{2} \) are the eccentricities of a hyperbola and its conjugate hyperbola, then the line always touches the circle \( x^{2}+ \) \( y^{2}=r^{2} \), where \( r= \)
(a) 1
(b) 2
(c) 3
(d) Cannot be decided
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