section_path: Analytic results/Equations/Cartesian coordinates/Equation of a circle
section_name: Equation of a circle
paragraph_text: Equation of a circle
  
  In an x – y Cartesian coordinate system, the circle with centre coordinates (a, b) and radius r is the set of all points (x, y) such that (x − a) 2 + (y − b) 2 = r 2. {\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}.}
  
  This equation, known as the equation of the circle, follows from the Pythagorean theorem applied to any point on the circle: as shown in the adjacent diagram, the radius is the hypotenuse of a right-angled triangle whose other sides are of length | x − a | and | y − b |. If the circle is centred at the origin (0, 0), then the equation simplifies to x 2 + y 2 = r 2. {\displaystyle x^{2}+y^{2}=r^{2}.}