SOLUTION: Find the equation of the locus of a point which moves such that its distance from (-3, 0) is one-half of its distance from (-8, 0).

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Question 886582: Find the equation of the locus of a point which moves such that its distance from (-3, 0) is one-half of its distance from (-8, 0).
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%2B3%29%5E2%2By%5E2=%281%2F4%29%28%28x%2B8%29%5E2%2By%5E2%29
%28x%2B3%29%5E2%2By%5E2=%281%2F4%29%28x%2B8%29%5E2%2B%281%2F4%29y%5E2
4%28x%2B3%29%5E2%2B4y%5E2=%28x%2B8%29%5E2%2By%5E2
4%28x%5E2%2B6x%2B9%29%2B3y%5E2=x%5E2%2B16x%2B64
4x%5E2%2B24x%2B36%2B3y%5E2=x%5E2%2B16x%2B64
3x%5E2%2B8x%2B36-64%2B3y%5E2=0
3x%5E2%2B8x%2B3y%5E2=28
Need to complete the square for x
3%28x%5E2%2B%288%2F3%29x%29%2B3y%5E2=28
3%28x%5E2%2B%288%2F3%29x%2B%283%2F4%29%5E2%29%2B3y%5E2=28%2B9%2F4
3%28x%2B3%2F4%29%5E2%2B3y%5E2=%28112%2B9%29%2F4
3%28x%2B3%2F4%29%5E2%2B3y%5E2=131%2F4
highlight%28%28x%2B3%2F4%29%5E2%2By%5E2=131%2F12%29