Symmetric Equation

Symmetric Equation

Algebraic equation in two variables such that the graphical representation of the corresponding function in the Cartesian plane remains the same when the two variables are interchanged.


  • The equation x² + y² = 100 is a symmetric equation. It is the equation of the relationship whose Cartesian graph is a circle centred at the origin and whose radius measures 10 units
    equation symetrique
  • Consider the equation y = 0.5x² – 3.
    The graphical representation of the corresponding function f(x) = 0.5x² – 3 is shown in red in the graph below :
    equation symetrique B
    Interchanging the two variables produces the equation x = 0.5y² – 3.
    The corresponding function is \(f\left( x\right) =\pm \sqrt {2x+3}\) whose graphical representation, in blue, is shown in the diagram above.
    Therefore, the equation y= 0.5x² – 3 is not symmetric since the graphs are not identical.

Try Buzzmath activities for free

and see how the platform can help you.