1. 11.7 – Parametric Equations
Precalculus
11.7 – Parametric Equations

2. Find the equation of the given graph using a parametric equation
The easiest way to write a parametric equation of a line is to set the interval to be 0 < t < 1
When t = 0, the graph needs to be at (1, 3) and when t = 1, the graph needs to be at (4, -2)
So far we have x(t) = 1 + a*t y(t) = 3 + b*t; 0 < t < 1 because this way when t = 0, x = 1 and y = 3
What “a” would make x = 4 when t = 1?
4 = 1 + a*1 3 = a
What “b” would make y = -2 when t = 1?
-2 = 3 + b*1 -5 = b
Thus the equation is x(t) = 1 + 3t y(t) = 3 – 5t; 0 < t < 1
Notice that <3, -5> is the vector from the first point to the second point!

3. Find the equation of the given graph using a parametric equation
Try this one on your own
Check by graphing on your calculator when you have your equation
Possible Answer:
x(t) = 4t y(t) = t 0 < t < 1

4. Find the equation of the given graph using a parametric equation
This is the graph of part of a circle
Notice that the center is at (-2, 1) and the radius is 5
Thus we have the equation x(t) = 5 cos(t) – 2 y(t) = 5 sin(t) + 1
In order to end up with just part of a circle we set the interval to match up with the angles (in radians)
0 < t < 3π/2
Thus the equation is x(t) = 5 cos(t) – 2 y(t) = 5 sin(t) < t < 3π/2

5. Find the equation of the given graph using a parametric equation
Try this one on your own
Check by graphing on your calculator when you have your equation
Possible Answer:
x(t) = 2 cos(t) y(t) = 6 sin(t) 0 < t < 2π