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Math Help - Describe the locus of z

  1. #1
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    Describe the locus of z

    | z - 12j | = 3 | z + 36 | if z is written in the form z = x+jy. What is the equation of the locus for z as a cartesian equation in terms of x and y

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  2. #2
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    Re: Describe the locus of z

    Geometrically, |z- a| is the distance from point z, in the complex plane, to point a. So |z- i| is the distance from the generic point z to i while |z+ 36| is the distance from z to -36. The locus is the set of points whose distance from i, (0, 1) in "xy" terms, is three times its distance from -36, (-36, 0) in "xy" terms.

    The distance from (x,y) to (0, 1) is \sqrt{x^2+ (y- 1)^2} and the distance from (x, y) to (-36, 0) is \sqrt{(x+ 36)^2+ y^2} so "|z- i|= 3|z+ 36|" is equivalent to \sqrt{x^2+ (y+1)^2}= 3\sqrt{(x+ 36)^2+ y^2}. Square both sides and the simplify.
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  3. #3
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    Re: Describe the locus of z

    What's happened to the 12 ?
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