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Describing a locus

  1. May 24, 2012 #1
    Hey guys, this is my problem:

    find the cartesian equation of the locus:

    |z-12i|/|z+36|=3

    So far ive got here:

    introduce z=x+iy then collect terms gives:

    √(x2+(y-12)2)=3√((x+36)2+y2)

    Squaring both sides I get:

    x2+(y-12)2=9(x+36)2+9y2

    This is where I am stumped... I've tried expanding it to see if I can factorise it into a standard circle, but I havn't been able to find a neat solution. Am I missing a trick here? Any help would be hugely appreciated as It's actually driving me insane!

    Thanks
     
  2. jcsd
  3. May 24, 2012 #2

    tiny-tim

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  4. May 24, 2012 #3
    Hey, thanks tiny-tim for your time and reply :), since I posted this I've had a good attempt at a solution... Let me know what you think perhaps?

    (x+40.5)^2 + (y+1.5)^2 = (405/2)^0.5

    I did this, as you said, by completing the square:

    i worked with this equation: x^2 + 81x + y^2 + 3y + 1440 = 0

    Any input is vastly appreciated, thank you :)
     
  5. May 24, 2012 #4

    tiny-tim

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    hey captainquarks! :smile:

    i'm just going to bed :zzz:, and i haven't had time to check your figures

    have you noticed that the original question is another way of writing "the distance from point a is 3 times the distance from point b" ? :wink:

    goodnight! :smile:
     
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