vertical line test

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The equation for a circle is not technically a function, because circles fail the vertical line test. If you like you can describe it as the combination of two functions with a restricted domain. e.g.  the circle x^2 + y^2 = 1 (the unit circle) could be written as the combination of y = +sqrt(-x^2 +1), y = -sqrt(-x^2 + 1). These functions draw the top half and the bottom half of the circle, respectively.  They are only defined in the real plane with x in the interval [-1,1]. So (x - h)^2 + (y - k)^2 = r^2 is how we write the equation of a circle, because not only is it shorter, it gives us valuable information about the radius and the center of the circle.