Aus Online Mathematik Brückenkurs 1

A circle is defined as all the points which have a fixed distance to the circle's midpoint. Hence, a point \displaystyle \left( x \right.,\left. y \right) lies on our circle if and only if its distance to the point \displaystyle \left( 1 \right.,\left. 3 \right) is exactly \displaystyle 2. Using the distance formula, we can express this condition as

\displaystyle \sqrt{\left( x-1 \right)^{2}+\left( y-2 \right)^{2}}=2

After squaring, we obtain the equation of the circle in standard form:

\displaystyle \left( x-1 \right)^{2}+\left( y-2 \right)^{2}=4