SOLUTION: Find the equation of the path of a point P(x,y) which moves so that its distance from (-3,0) is one-half its distance from the line x=-12. Thank you!!!!

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the equation of the path of a point P(x,y) which moves so that its distance from (-3,0) is one-half its distance from the line x=-12. Thank you!!!!      Log On


   

Question 895993: Find the equation of the path of a point P(x,y) which moves so that its distance from (-3,0) is one-half its distance from the line x=-12. Thank you!!!!
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Variable point P(x,y).
The line x=-12 is the variable point (-12,y).


sqrt%28%28x%2B3%29%5E2%2By%5E2%29=%281%2F2%29sqrt%28%28x%2B12%29%5E2%2B0%29

%28%28x%2B3%29%5E2%2By%5E2%29=%281%2F4%29%28%28x%2B12%29%5E2%29

4%28x%2B3%29%5E2%2B4y%5E2=%28x%2B12%29%5E2
4%28x%5E2%2B6x%2B9%29%2By%5E2=x%5E2%2B24x%2B144
4x%5E2%2B24x%2B36%2By%5E2=x%5E2%2B24x%2B144
3x%5E3%2B36%2By%5E2=144
3x%5E2%2By%5E2=108
highlight%28x%5E2%2F36%2By%5E2%2F108=1%29