Find the equation that represents all of the points that are three times as far from (6,6) as they are from (2,0)
Let such a point be P(x,y)
then
√((x-6)^2 + (y-6)^2) = 3√((x-2)^2 + y^2)
square both sides and expand
x^2 - 12x + 36 + y^2 - 12y + 36 = 9x^2 - 36x + 36 + 9y^2
8x^2 + 8y^2 - 24x + 12y = 36
Sure looks like a circle.
I converted this to the standard form of a circle
(x - 3/2)^2 + (y + 3/4)^2 = 117/16
so the centre of our circle is (3/2 , -3/4) and its radius is √117/4