Parametric Equations
Parametric equations express the coordinates of a curve as separate functions of a third variable (the parameter), allowing description of complex paths and motion.
What You Need to Know
Key Concept Diagram
In parametric form, x = f(t) and y = g(t), where t is the parameter
The parameter often represents time, describing the position of a moving object
To eliminate the parameter, solve one equation for t and substitute into the other
Parametric curves can describe paths that are not functions in standard form
The direction of travel along a parametric curve depends on how the parameter increases
Key Vocabulary
Parameter
A variable (often t) that is used to define both x and y coordinates of a curve
Parametric equations
A pair of equations expressing x and y each as functions of a common parameter
Cartesian form
The standard equation of a curve expressed directly in terms of x and y
Eliminating the parameter
The process of combining parametric equations to produce a single Cartesian equation
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Given x = 2t and y = t^2, eliminate the parameter to find the Cartesian equation.
Question 2
The parametric equations x = cos(t), y = sin(t) describe which curve?
Question 3
If x = t + 1 and y = 2t - 3, what is the Cartesian equation?
Key Concepts Summary
- ●In parametric form, x = f(t) and y = g(t), where t is the parameter
- ●The parameter often represents time, describing the position of a moving object
- ●To eliminate the parameter, solve one equation for t and substitute into the other
- ●Parametric curves can describe paths that are not functions in standard form
- ●The direction of travel along a parametric curve depends on how the parameter increases