The Position of a Sonic Boom Caused by the Faster-Than-Sound $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Essay

The position of a sonic boom caused by the faster-than-sound aircraft is the hyperbola $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$ in the coordinate system shown. How wide is the hyperbola 2 units from its vertex?
$1 + \log _ { 4 } 9 x - \log _ { 4 } y$