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Math Help - Compound Locus

  1. #1
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    Compound Locus

    (1) What is a locus.

    (2) What is compound locus?

    QUESTION:

    Two points A and B are 6 units apart. How many points are there that are equidistant from both A and B and also 5 units from A?
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  2. #2
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    Quote Originally Posted by symmetry View Post
    (1) What is a locus.

    (2) What is compound locus?

    QUESTION:

    Two points A and B are 6 units apart. How many points are there that are equidistant from both A and B and also 5 units from A?
    Locus and compound locus?
    For definitions, search Google or Wikipedia or Yahoo.

    ---------------
    The Question:

    The locus of points that are 5 units from A is a circle whose center is A.

    The locus of points that are equidistant from both A and B is the perpendicular bisector of line AB.

    The intersection of these two loci answers your question.

    The equation of the circle whose center is A and whose radius is 5 units, if the origin (0,0) is at A, is
    x^2 +y^2 = 5^2
    x^2 +y^2 = 25 -----------first locus.

    If A again is the origin (0,0), the perpendicular bisector of line AB is
    x = 6/2
    x = 3 ---------------------second locus

    Their intersection:
    Substitute 3 for x in the first locus,
    3^2 +y^2 = 25
    y^2 = 25 -9 = 16
    y = +4 or -4

    So there are two intersection points, (3,4) and (3,-4)

    Therefore, two points. -----------answer.
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  3. #3
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    ok

    A locus could be a line, an equation, etc?
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  4. #4
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    Quote Originally Posted by symmetry View Post
    A locus could be a line, an equation, etc?
    Have you searched at least Google for "locus"?

    Here is one from Google:
    "A locus is the set of all points (usually forming a curve or surface) satisfying some condition. For example, the locus of points in the plane equidistant from a given point is a circle, and the set of points in three-space equidistant from a given point is a sphere."

    Locus means the locations/positions of a set of points satisfying some condition.

    "locus" ---"location"

    And, yes, a locus of points can be a line, a curved line, a surface,.....
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  5. #5
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    ok

    Okay...I will study locus more deeply.
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