# Lecture 5: Parametric equations for lines and curves.

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Lesson Summary:

In this lesson, we learn how to write parametric equations for lines and curves. We start by looking at lines in space and thinking of them as the trajectory of a moving point. We then use this idea to find formulas for the position of the moving point in terms of time, giving us a parametric equation for the line. We also explore how to use parametric equations to find the intersection of a line and a plane. Finally, we see an example of using parametric equations for an arbitrary motion in space, such as the cycloid curve.

Lesson Description:

Learn how to write parametric equations for lines and curves.

Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 15, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.

• How do you write a parametric equation for a line?
• How do you write a parametric equation for a curve?
• What is an application of using parametric equations to describe a line?
• How can you find where a line intersects a plane?
• What is a cycloid and how is it obtained?
• What shape does a point on the rim of a moving wheel make?
• What is the position of a point on a wheel as a function of the angle that the wheel has rotated?
• #### Staff Review

• Currently 4.0/5 Stars.
This lesson does a great job of explaining parametric equations for lines and curves. This is such an important concept in Calculus, and you can learn how it is done in this lesson. Also, some applications for parametric equations are discussed, including the cycloid in depth.