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Math Help - Conic Sections

  1. #1
    Junior Member
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    Conic Sections

    Hey..I don't understand conic sections at all...

    1.
    Find a polynomial equation with integer coeffiecients for the set of coplanar points desscribed. Tell whether or not the graph is a conic section and, if it is, tell which conic section.

    For each point, its distance from the fixed point (4,3) is 3 times its disstance from the fixed point (-1,2).
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  2. #2
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    Hello, Trentt!

    1. Find a polynomial equation with integer coeffiecients
    for the set of coplanar points described.
    Tell whether or not the graph is a conic section and, if it is, tell which conic section.

    For each point, its distance from the fixed point A:(4,3)
    is 3 times its distance from the fixed point B:(-1,2).

    Let the variable point be P:(x,y).
    Then: .PA .= .3PB
    . . . . . . . . ._______________ . . . . . . _______________
    We have: .√(x - 4) + (y - 3) . = . 3√(x + 1) + (y - 2)

    Square both sides: .x - 8x + 16 + y - 6y + 9 .= .9x + 18x + 9 + 9y - 36y + 36

    And we have: .8x + 8y + 26x - 30y + 20 .= .0 . . 4x + 4y + 13x - 15y + 10 .= .0

    Since the coefficients of x and y are equal, the conic is a circle.
    . . In fact, it is called a Circle of Apollonius.

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