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Math Help - locus points

  1. #1
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    locus points

    The locus of the points (x,y) satisfying the relationship

    |z| = 2|z-1|

    is

    A region exterior to a circle

    or

    A region interior to a circle

    or

    A circle

    many thanks
    ck
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  2. #2
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    If z= x+ iy, then |z|= \sqrt{x^2+ y^2} and |z- 1|= \sqrt{(x- 1)^2+ y^2} so your equation says that \sqrt{x^2+ y^2}= 2\sqrt{(x-1)^2+ y^2}. Square both sides of that and reduce. What figure is that?

    But with "multiple choice" you should be able to look at that equation and get the answer simply by the fact that it is and equation!
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    If z= x+ iy, then |z|= \sqrt{x^2+ y^2} and |z- 1|= \sqrt{(x- 1)^2+ y^2} so your equation says that \sqrt{x^2+ y^2}= 2\sqrt{(x-1)^2+ y^2}. Square both sides of that and reduce. What figure is that?

    But with "multiple choice" you should be able to look at that equation and get the answer simply by the fact that it is and equation!
    hi HallsofIvy,

    x^2 + y^2 = constant <--- this is a circle equation...

    from the hints you gave, i had achieve the same answer and working but i can't conclude which is the correct answer... is "A circle" wrong ?
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  4. #4
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    Quote Originally Posted by Chris0724 View Post
    hi HallsofIvy,

    x^2 + y^2 = constant <--- this is a circle equation...

    from the hints you gave, i had achieve the same answer and working but i can't conclude which is the correct answer... is "A circle" wrong ?
    You found that it's a circle. So why are you having trouble choosing the correct option?!
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