When flying faster than the speed of light, an airplane that flies parallel to the ground forms sound waves in the shape of a cone behind it. The waves intersect the ground in the shape of a hyperbola, with the airplane directly above the center of this hyperbola. If you hear a sonic boom along the hyperbola x^2/81 - y^2/4 = 1, what is the shortest horizontal distance you could be to the airplane?

show work please!!