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For each point in a set of points, its distance from (3,4) is four times it's distance from (-5,2)

a. Find the equation
b. tell which conic section the graph will be.

  • Math/conics -

    let d1 = distance of (x,y) from (3,4)
    d1^2 = (x-3)^2 + (y-4)^2

    let d2 = distance from (-5,2)
    d2^2 = (x+5)^2 + (y-2)^2

    since d1 = 4*d2
    d1^2 = 16*d2^2

    (x-3)^2 + (y-4)^2 = 16[(x+5)^2 + (y-2)^2]

    expand and collect terms to arrive at

    (x+83/15)^2 + (y-28/15)^2 = 7234/15

    Looks like a circle

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