Answer:
Step-by-step explanation:
A hyperbola is a curve for which the difference of the distances |d₂ - d₁| of any point P from the foci is constant.
The definition leads to the equation
1. Calculate the value of a²
Assume the neighbours are at the foci A and B.
The explosion is farther from B than from A, so it occurred on the right branch of the hyperbola.
Then AB = 1 mi = 5280 ft
and the distance from the focus to the y-axis is
c = 2640
The vertices are (±a,0).
The speed of sound is 1100 ft/s, so B is 2200 ft further from the explosion.
The distance from A to the vertex V₁ is c - a. Then
AB = 2200 + 2(c - a) = 2200 -2(2640 - 2a) = 2200 +5280- 2a = 5280
2a = 2200
a = 1100
a² = 1 210 000
2. Calculate the value of b²
3. Write the equation for the hyperbola
