Posted by Tiffany on Monday, April 2, 2012 at 10:33pm.
Suppose lighthouse A is located at the origin and lighthouse B is located at coordinates (0,6). The captain of a ship has determined that the ship's distance from lighthouse A is 2 and its distance from lighthouse B is 5. What are the possible coordinates for the ship?

calculus  Reiny, Monday, April 2, 2012 at 11:41pm
Let the coordinates of the ship be P(x,y)
so AP =2 and BP=5
√(x^2+y^2) = 2
x^2+y^2 = 4 , (#1)
√( (x^2 + (y6)^2 ) = 5
x^2 + y^2  12y + 36 = 25
x^2 + y^2  12y = 11 , (#2)
#1  #2 :
12y = 15
y = 15/12 = 5/4 = 1.25
then in #1:
x^2 + 225/144 = 4
x^2 = 39/16
x = ± √39/4
The ship could be at (√39/4 , 5/4) or (√39/4 , 5/4)