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conics

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given O(0,0) and N(12,0) write an equation in terms of x and y for all points P(x,y) such that segment PO is perpendicular to segment PN. simplify this equation and show that P is on a circle.

  • conics -

    slope of PO= y/x

    slope of PN = y/(x-12)

    For segments to be perpendicular their slopes must be negative recipricols

    Thus, -x/y=y/(x-12)

    y^2+x(x-12)=0

    Distribute the x, complete the square, and then you'll have the equation of a circle.

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