Please help I'm really stuck on this problem and want to do well. 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^2/100 - y^2/4= 1, what is the shortest horizontal distance you could be to the airplane?

Please show your work, I want to learn how to do this.