hyperbola and cricle

Level pending

If a variable line has its intercepts on the coordinate axes \(e,e_{1}\) , where \(\frac {e}{2} , \frac{e_{1}}{2}\) are the eccentricities of a hyperbola and its conjugate hyperbola respectively, the the line always touches the circle \(x^2+y^2=r^2\). What is the value of \(r\) ?

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