# 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.

### Examples

• 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
• 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 :

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.