(a)

Find the equation of the hyperbola:

Emmett and Carson are located on the -axis.

Standard from of horizontal hyperbola is  .

The distance between Emmett and Carson is 3 miles.

Convert the miles in feet.

.

           .

They are located at focus of hyperbola.

.

Find values.

The absolute value of the difference of the distances from any point on a hyperbola to the foci is .

The sound travels at 1100 feet per second.

.

.

Substitute in .

The hyperbola equation is .

(b)

Since Emmett heard tthe finale before Carson did and Emmitts location is to the right of the origin on the  -axis, the fireworks display was located on the right branch of the hyperbola.

(a).

(b) on the right branch.