SOLUTION: Plss help me to solve this problem Two ground stations are located by its coordinates as A(0,0) and B(0,5),the unit being 1km. An airplane pilot conducting a reconnaisance survey

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Plss help me to solve this problem Two ground stations are located by its coordinates as A(0,0) and B(0,5),the unit being 1km. An airplane pilot conducting a reconnaisance survey       Log On


   

Question 1046576: Plss help me to solve this problem
Two ground stations are located by its coordinates as A(0,0) and B(0,5),the unit being 1km. An airplane pilot conducting a reconnaisance survey knows from the radar that at a certain instant he is 3 km. nearer B than A. What is the equation of the curve that defines this data? I hope you will answer this question. Thanks.
Found 2 solutions by Alan3354, Fombitz:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The locus of points with a constant difference as stated is the definition of a hyperbola.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So assume the plane is at (x,y).
The distance from A to the plane is D%5BA%5D=sqrt%28%28x-0%29%5E2%2B%28y-0%29%5E2%29=sqrt%28x%5E2%2By%5E2%29.
The distance from B to the plane is D%5BB%5D=sqrt%28%28x-0%29%5E2%2B%28y-5%29%5E2%29=sqrt%28x%5E2%2B%28y-5%29%5E2%29.
You also know that,
D%5BB%5D=D%5BA%5D%2B3
sqrt%28x%5E2%2B%28y-5%29%5E2%29=sqrt%28x%5E2%2By%5E2%29%2B3