section_path: Analytic results/Equations/Cartesian coordinates/Homogeneous form
section_name: Homogeneous form
paragraph_text: Homogeneous form
  
  In homogeneous coordinates, each conic section with the equation of a circle has the form x 2 + y 2 − 2 a x z − 2 b y z + c z 2 = 0. {\displaystyle x^{2}+y^{2}-2axz-2byz+cz^{2}=0.}
  
  It can be proven that a conic section is a circle exactly when it contains (when extended to the complex projective plane) the points I (1: i: 0) and J (1: − i: 0). These points are called the circular points at infinity.