listening station A and listening station B are located at (3300, 0) and (-3300, 0), respectively. Station A detects an explosion 4 seconds before station B. (Assume the coordinate system is measured in feet and sound travels at 1100 feet per second.) Where did the explosion occur? (Write an equation for the hyperbola that describes where the explosion could have occurred.)

Answer: (3300, - 2750)

Explanation:

Since Station A detects an explosion 4 seconds before station B. and sound travels at 1100 feet per second.

c + a - (c - a) = 4 * 1100

2a = 4400

a = 2200

Using pythagorean theorem to get b

b^2 = c^2 + a^2

b^2 = 3300^2 + 2200^2

b = 6050000

The x-coordinate of the explosion must be 3300. The y-coordinate must also be negative since the first station detects the explosion first.

equation for the hyperbola is

X^2/a^2 + Y^2/b^2 = 1

Explosion must occur at x-axis. (3300)

Substitutes x, a and b into the equation to get y

3300^2/4840000-y^2/6050000 = 1

2.25 - y^2/6050000 = 1

y^2 = 6050000 * 1.25

y^2 = 7562500

y = + / -2750

Since y must be negative

Therefore, the explosion will occur at (3300, - 2750)