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another application of the distance formula is the derivation of the equation of a circle now we say the equation of the circle sometimes but other people prefer to say the standard form of a circle because in fact circles have lots of different representations and this is only one of them it turns out to be extremely useful because it tells us a lot of information about the circle well what is a circle it circles the set of points x y that are some fixed distance r away some from some fixed point in this case well call this point here h k x y is a generic point representing all the points on the circle and r is the radius where the distance between the center to any point on the circle so if we look at the distance formula we have that the distance between any two points is equal to the square root of x2 minus x1 squared plus y2 minus y1 squared now for this particular application what were going to do is were going to square both sides of this equation so when we square we elimina