conics
posted by tatiana .
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.

slope of PO= y/x
slope of PN = y/(x12)
For segments to be perpendicular their slopes must be negative recipricols
Thus, x/y=y/(x12)
y^2+x(x12)=0
Distribute the x, complete the square, and then you'll have the equation of a circle.