Asked by Tiffany
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?
Answers
Answered by
Reiny
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 + (y-6)^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)
so AP =2 and BP=5
√(x^2+y^2) = 2
x^2+y^2 = 4 , (#1)
√( (x^2 + (y-6)^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)
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.