Angela G.

asked • 10/26/20

Hyperbola word problem. Needing answers and explanations

A ship is located 30 miles from a straight shoreline. LORAN stations are located at point A and B on the shoreline, 220 miles apart. From the LORAn signals, the captain determines that the ship is 50 miles closer to station A than to station B. What is the location of the ship? (Place ‘A’ and ‘B’ on the y-axis with the x-axis halfway between them. Find the ‘x’ and ‘y’ coordinates of the ship)


Paul M.

tutor
I don't see the analytic solution yet; I will work on it. But graphically, the y co-ordinate of the ship is between 25.9 and 26.
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10/26/20

Paul M.

tutor
I have thought about this for quite a while and see no way to solve this analytically. When you review it in class, I would certainly appreciate some feedback. Thank you.
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10/26/20

1 Expert Answer

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Mark M. answered • 10/27/20

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Mathematics Teacher - NCLB Highly Qualified

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Draw and label a diagram.

S is the ship at (x, y) it is in QI

A is (0, 110)

B is (o, -110

The point on the shore 30 miles from the ship is (30, y)

The distance from the ship to B is "h"

The distance from the ship to A is "h - 50"


Using Pythagoras


302 + (110 + y) = h2

302 + (110 - y)2 = (h - 50)2


Now solve for y.

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