page_title: Cassini oval
section_title: Formal definition
hierarchical_section_title: Cassini oval / Formal definition
context_page_description: A Cassini oval is a quartic plane curve defined as the set of points in the plane such that the product of the distances to two fixed points is constant. This may be contrasted with an ellipse, for which the
  sum of the distances is constant, rather than the product. Cassini ovals are the special case of polynomial lemniscates when the polynomial used has degree 2.
  Cassini ovals are named after the astronomer Giovanni Domenico Cassini who studied them in 1680.
  Cassini believed that the Sun traveled around the Earth on one of these ovals, with the Earth at one focus of the oval.
  Other names include Cassinian ovals, Cassinian curves and ovals of Cassini.
context_section_description: A Cassini oval is a set of points, such that for any point  of the set, the product of the distances  to two fixed points , is constant, usually denoted by :
  As with an ellipse, the fixed points  are called the foci of the Cassini oval.
caption: Cassini oval: 
    
      
        
          
            |
          
          P
          
            P
            
              1
            
          
          
            |
          
          ⋅
          
            |
          
          P
          
            P
            
              2
            
          
          
            |
          
          =
          
            b
            
              2
            
          
        
      
      {\displaystyle |PP_{1}|\cdot |PP_{2}|=b^{2}}
    
   for any location of P on the curve