This lesson includes 6 additional questions and 29 additional question variations for subscribers.
Lesson Worksheet: Conversion between Parametric and Rectangular Equations Mathematics • 12th Grade
In this worksheet, we will practice converting from the parametric form of an equation to its equivalent rectangular form and vice versa.
Q1:
Use the fact that to find a parametrization of the part of the hyperbola that contains the point .
- A
- B
- C
- D
- E
Q2:
The first figure shows the graphs of and that parameterize the unit circle for . What do the two functions graphed in the second figure parameterize?
- AThe unit circle
- BThe square on , , ,
- CThe square on , , ,
- DThe square on , , ,
Q3:
Consider the points and .
What is the length of ?
Find a parameterization of the segment over .
- A
- B
- C
- D
- E
Find and so that , parameterizes over .
- A
- B
- C
- D
- E
Using the functions above for , what is the distance between the point and the point ?
- A
- B
- C
- D
- E
The parameterization of above is an example of an {arc-length parameterization} of a plane curve. Find an arc-length parameterization , of , where and the parameter starts at . Give the interval used.
- A on
- B on
- C on
- D on
- E on
Q4:
A particle moves along the curve given by the parametric equations , with .
At which point is the particle located when ? Give your answer to one decimal place, if necessary.
- A
- B
- C
- D
- E
At which points is the particle located when and ? Give your answers to one decimal place, if necessary.
- A and
- B and
- C and
- D and
- E and
Find an equation for the line that the particle moves along in the form .
- A
- B
- C
- D
- E
What is the smallest value of during the particle’s motion? When is it reached?
- A, at
- B, at
- C, at
- D, at
- E, at
Describe the motion from to in terms of position on the line.
- AThe particle starts at , goes left and upward to , and then goes back right and downward to .
- BThe particle starts at , goes left and upward to , and then goes back right and downward to .
- CThe particle starts at , goes right and downward to , and then goes back left and upward to .
- DThe particle starts at , goes left and upward to , and then goes back right and downward to .
- EThe particle starts at , goes right and downward to , and then goes back left and upward to .
Give the parameters , that describe the same motion but on an interval starting at instead of . In what interval does lie?
- A, , the interval
- B, , the interval
- C, , the interval
- D, , the interval
- E, , the interval
Q9:
Convert the rectangular equation to parametric form.
- A
- B
- C
- D
- E