|
Question 1068652: I've got two LORAN stations A and B that are 500 miles apart. A and B are also the Foci of a hyperbola. A ship at point P (which lies on the hyperbola branch with A as the focus) receives a nav signal from station A 2640 micro-sec before it receives from B. If the signal travels 980 ft/microsecond, how far away is P from A and B? Also, what are the values for a, b, and c? Show your illustration.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! The difference in the distances from any point on a hyperbole to the foci is a constant - by convention the first distance is to the furthest focus
:
(a + c) – (c – a) = 2a
:
the distance from the center to either focus is c = 250 miles
:
we can place the center of the hyperbole at the origin of its graph - this means we have h = k = 0
:
2a = 2640 * 980 = 2587200
a = 1293600 ft = 1293600 / 5280 = 245 miles
:
for hyperbola's b^2 = c^2 - a^2
:
b^2 = 250^2 - 245^2 = 2475
b = 49.74937 approximately 49.75
:
*****************************************************
distance from P to A is c - a = 250 - 245 = 5 miles
:
distance from P to B is c + a = 250 + 245 = 495 miles
:
a = 245 miles
b = 49.75 miles
c = 250 miles
******************************************************
:
|
|
|
| |
