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Parametric functions describe a curve by expressing its coordinates as separate functions of a third variable, often called a parameter. Instead of writing one variable directly in terms of another, we define both x and y (or more variables) in terms of this parameter, usually t. This allows us to represent complex curves that cannot be described easily by a single equation, such as circles, ellipses, or spirals. As t changes, the pair of values (x(t), y(t)) traces the path of the curve, giving