A line touches a hyperbola at P and intersects the pair of asymptotes at points Q and R. If equation of pair of asymptotes is given by $4x^2+8xy-y^2=0$ and mid-point of QR is (1,0), then

Equation of hyperbola is given by $4x^2+8xy-y^2-4=0$

If circumcenter of $\Delta OQR$ is (a, b) then a + 9b = 4, (O is center of hyperbola)

If circumcenter of $\Delta OQR$ is (a, b) then a – b = -1; (O is center of hyperbola)

Length of transverse axis of hyperbola is $\frac{\sqrt{89}-3}{10}$