# 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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