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On a rectangular hyperbola x^(2)-y^(2)=a...

On a rectangular hyperbola `x^(2)-y^(2)=a^(2),a gt 0`, three points A,B,C are taken as follows : A = (-a,0): B and C are placed symmetrically with respect to the x-axis on the branch of the hyperbola not containing A suppose that the triangle ABC is equilateral. If the side-length of the triangle ABC is ka,then k lies in the interval

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