On a rectangular hyperbola x2–y2=a2,a>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

On a rectangular hyperbola x2–y2=a2,a>0, three points A,B,C are take

1.	On a rectangular hyperbola x2–y2=a2,a>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
Answer» On a rectangular hyperbola $x^{2} - y^{2} = a^{2}, a > 0$ , 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 $A B C$ is equilateral. If the side-length of the triangle $A B C$ is $k a$ , then $k$ lies in the interval