If a variable line has its intercepts on the coordinate axes e and e' , where e2 and e'2 are the eccentricities of a hyperbola and its conjugate hyperbola, then the line always touches the circle x2+y2=r2, where r =

Since e2 and ee'2 are the eccentricities of a hyperbola andits conjugate hyperbola, we have4e2+4e′2=1or  4=e2e′2e2+e′2The line passing through the points (e, 0) and (0, e') ise′x+ey−ee′=0It is tangent to the circle x2+y2=r2 Hence,ee′e2+e′2=ror  r2=e2e′2e2+e′2=4or  r=2