Parametric Equations

Definition: A parametric equation is used when a function in x and y is defined through a third variable, usually t, called the parameter:

x = f(t)

y = g(t)

Functions can be defined using parametric equations or rectangular coordinates (x, y). They can be converted between one another through substitution to eliminate the parameter.

Example: Eliminate the parameter t.

x = t/2, y = t² + 2


Step 1: To eliminate the parameter, we must first isolate t from one of the equations.

x = t/2
2x = t

Step 2: Substitute t = 2x  into the second equation.

y = t² + 2

y = (2x)² + 2

y = 4x² + 2

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