Parametric Equations Practice Quiz
1. For each of the following, determine the type of equation it is, parametric or rectangular.
a.
This is a parametric equation. We know this because there are two equations as opposed
to just one.
b.
This is a rectangular equation because there is only one equation – this is in the form we
are familiar with.
c.
This is a parametric equation. It is not important that the letters are different. What is
important is two equations versus one.
d.
We are used to defining equations as
this is still a rectangular equation.
something, but that doesn’t change the fact that
e.
This is a rectangular equation despite the letters being different.
2. Convert the following to a rectangular equation.
We first solve for :
We now substitute in for to the other equation:
And simplify:
3. Eliminate the parameter for the parametric equations
.
and
, where
Solve for :
Substitute in:
Simplify:
4. Eliminate the parameter for the parametric equations
.’
Solve for :
Substitute in:
Simplify:
5. Convert the following to a rectangular equation.
Solve for :
Substitute in:
Simplify:
and
, where
6. Write a set of parametric equations for
.
We can take the easy way out of this and define,
be:
. That would make our set of equations
Another option could be to set
, meaning
That would make our set of equations:
.
7. Write two sets of parametric equations for
The easy way out of this would be to say:
Another option would be to say:
We could also say,
, in this case, our equations would be:
, so our equations would be:
There are many other possible answers you could have.
8. Find two sets of parametric equations for
.
The easiest answer would be:
Another answer would be to set
This would give us:
, so
9. Find the coordinates of the point on the plane curve described by
for when
.
We will simply substitute in
and
:
That gives us our ordered pair:
.
10. Use point plotting to graph the plane curve described by the parametric equations
over the domain
.
Setting up our table would look like
this:
The graph looks like this:
11. Use point plotting to graph the plane curve described by the parametric equations
over the interval
.
Setting up our table would look like
this:
and
and
The graph looks like this:
12. Bonus: Review the history of complex numbers.
Study your notes from the first day of class, or review the PowerPoint from that day which is
uploaded to the web site.