SOLUTION: I'm working on the following question. "find the equation of the set of all points P(x,y) that the difference of the distance from (-3,4) and (3,4) is 4. I've started as follows

Algebra ->  Circles -> SOLUTION: I'm working on the following question. "find the equation of the set of all points P(x,y) that the difference of the distance from (-3,4) and (3,4) is 4. I've started as follows      Log On


   

Question 944672: I'm working on the following question. "find the equation of the set of all points P(x,y) that the difference of the distance from (-3,4) and (3,4) is 4.
I've started as follows:
+sqrt%28%28-3-x%29%5E2%2B%284-y%29%5E2%29-sqrt%28%283-x%29%5E2%2B%284-Y%29%5E2%29=4+
from there i've simplified to :

I'm lost from here. Any help would be greatly appreciated.
Found 2 solutions by amarjeeth123, MathLover1:
Answer by amarjeeth123(570) About Me  (Show Source):
You can put this solution on YOUR website!
We get
x^2+y^2+6x-8y+25=16+x^2+y^2-6x-8y+25+8sqrt(x^2+y^2-6x-8y+25)
12x-16=8sqrt(x^2+y^2-6x-8y+25)
3x-4=2sqrt(x^2+y^2-6x-8y+25)
Squaring on both sides
9x^2+16-24x=4(x^2+y^2-6x-8y+25)
5x^2-4y^2+32y-84=0

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!






6x%2B25+=+-6x%2B8sqrt%28x%5E2-6x%2By%5E2-8y%2B25%29%2B41

6x%2B25+%2B6x-41=8sqrt%28x%5E2-6x%2By%5E2-8y%2B25%29

12x-16=8sqrt%28x%5E2-6x%2By%5E2-8y%2B25%29 square both sides

%2812x-16%29%5E2=8%5E2%28sqrt%28x%5E2-6x%2By%5E2-8y%2B25%29%29%5E2

144x%5E2-384x%2B256=64%28x%5E2-6x%2By%5E2-8y%2B25%29

144x%5E2-cross%28384x%29%2B256=64x%5E2-cross%28384x%29%2B64y%5E2-512y%2B1600

144x%5E2%2B256-64x%5E2-64y%5E2%2B512y-1600=0

80x%5E2-64y%5E2%2B512y-1344=0 simplify, divide by 16

5x%5E2-4y%5E2%2B32y-84=0