Lesson 11 ­ Parametric Equations
Do Now: Pre­Calc
Given the equation of the line below, state a point on the line, the slope of the line, write a vector equation, and parametric equations for the line.
Point & Slope:
Vector Equation:
Parametric Equations:
Verify:
1
Lesson 11 ­ Parametric Equations
Parametric Equations
Parametric Equations can be used to find point on a line in both and . In the Do Now, we found the parametric equations for the line given the equation of the line. To find the parametric equations, we needed to know:
1. The slope 2. A point
We can also find the parametric equation for a line when given:
1. A point
2. A direction vector
2
Lesson 11 ­ Parametric Equations
In , the parametric equations of a line through the point (x1,y1) in the direction of vector
can be derived from the vector equation: In , the parametric equations of a line through the point (x1,y1,z1) in the direction of vector
can be derived from the vector equation: 3
Lesson 11 ­ Parametric Equations
Examples:
1. Find the parametric equations of the line through the point P(1,1) in the direction of vector .
Examples:
2. Find the parametric equations of the line through the point P(2,3,1) in the direction of
vector .
4
Lesson 11 ­ Parametric Equations
How can we find the parametric equations for a line if all we are given is two points on the line?
1. Find the direction vector between the two points.
2. Using a point and the direction vector, find the parametric equations.
5
Lesson 11 ­ Parametric Equations
Examples:
1. Find the parametric equations of the line through the points P(1,1) and Q(­1,4).
Examples:
2. Find the parametric equations of the line through the points P(1,2,3) and Q(­4,1,0).
6