Understanding Parametric Equations
Choose your learning level
Watch & Learn
Video explanation of this concept
concept. Use space or enter to play video.
Beginner
Start here! Easy to understand
Now showing Beginner level explanation.
Beginner Explanation
Parametric equations define x and y in terms of a parameter t. For example, x = t and y = t^2 + 5 traces the parabola y = x^2 + 5 as t varies over real numbers.
Practice Problems
Test your understanding with practice problems
1
Quick Quiz
Single Choice Quiz
Beginner
Which set of parametric equations represents $y = x^2 + 5$?
Please select an answer for all 1 questions before checking your answers. 1 question remaining.
2
Real-World Problem
Question Exercise
Intermediate
Car Path
A car travels along a path described by $x = t + 5$ and $y = t^2$ for t in [0, 5]. Eliminate the parameter to find the rectangular equation of the path.
Click to reveal the detailed solution for this question exercise.
3
Thinking Challenge
Thinking Exercise
Intermediate
Think About This
Describe the curve formed by $x = \cos(t)$ and $y = \sin(t)$.
Click to reveal the detailed explanation for this thinking exercise.
4
Challenge Quiz
Single Choice Quiz
Advanced
Which of the following parametric equations represents a hyperbola?
Please select an answer for all 1 questions before checking your answers. 1 question remaining.
Recap
Watch & Learn
Review key concepts and takeaways