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(a)
To write: The equation of the hyperbola centered the origin on which the plane is located.
(a)
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Answer to Problem 14CFU
Explanation of Solution
Given information: Aviation: Airplanes are equipped with signal devices to alert rescuers to their position. Suppose a downed plane sends out radio pulses that are detected by two receiving stations A and B . the stations are located 130 miles apart along a stretch of I-40 with A due west of B . the two stations are able to determine that the plane is 50 miles farther from station B than from station A .
Calculation:
Sketching out a drawing, the important piece of information is not only that the stations (foci) are 130 miles apart ( c = 65), but that the distance to the ship is 50 more for station B .
The difference between the distance from A to the plane and B to the ship is 50.
So,
Centered at the origin gives us:
Since:
This gives us finally:
(b)
To graph: The equation, indicating on which branch of the hyperbola the plane is located.
(b)
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Answer to Problem 14CFU
The graph
Explanation of Solution
Given information: Aviation: Airplanes are equipped with signal devices to alert rescuers to their position. Suppose a downed plane sends out radio pulses that are detected by two receiving stations A and B . the stations are located 130 miles apart along a stretch of I-40 with A due west of B . the two stations are able to determine that the plane is 50 miles farther from station B than from station A .
Calculation:
(c)
To find: The exact coordinates of its position, if the pilot estimates that the plane is 6 miles from I-40.
(c)
![Check Mark](/static/check-mark.png)
Answer to Problem 14CFU
Plane’s coordinates:
Explanation of Solution
Given information: Aviation: Airplanes are equipped with signal devices to alert rescuers to their position. Suppose a downed plane sends out radio pulses that are detected by two receiving stations A and B . the stations are located 130 miles apart along a stretch of I-40 with A due west of B . the two stations are able to determine that the plane is 50 miles farther from station B than from station A .
Calculation:
If the plane is 6 miles from the axis (I-40), then y = 6 at that point.
Plug in 6 for y and solve for x .
Since we are in quadrant 2, we’ll keep the negative.
Plane’s coordinates:
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Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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