Question 1

Sketch the plane curve defined by the given parametric equations.  
A) 
B) 
C) 
D)

Accepted Answer

A

Question 2

Find parametric equations describing the given curve.
The line segment from  to

Accepted Answer

Answers may vary. One possible answer follows.

Question 3

Find parametric equations describing the given curve.
The portion of the parabola  from  to

Accepted Answer

Answers may vary. One possible answer follows.

Question 4

Sketch the plane curve defined by the given parametric equations.  
A) 
B) 
C) 
D)

Accepted Answer

When we eliminate the parameter t between the equations x = 5t and y = t^2, we get y = x^2/25. This is the equation of a parabola that opens upwards, with vertex at the origin and axis of symmetry along the x-axis. The point (5,25) lies on the curve, which means it is the highest point of the parabola. Therefore, choice B is the best match, as it shows a parabolic curve that opens upwards, with a visible vertex at the origin, and reaches the point (5,25). Choice A shows a curve that is not symmetrical, and choices C and D show curves that are too steep and do not reach the given point.

Question 5

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5]. 
A) 
B) 17 
C) 
D)

Accepted Answer

By observing the given parametric equations, we recognize them as the parametric equations of a circle centered at (2,1) with radius 3. Therefore, the best choice is C, which shows a circle with center (2,1) and radius 3, with the given window size.

Question 6

For the given parametric equations, find a corresponding x-y equation for the curve. 
A) 
B) 
C) 
D)

Accepted Answer

We can use the parametric equations to eliminate the parameter t and get an x-y equation. 
Starting with x = 2t + 1, we can isolate t: t = (x-1)/2 
Substituting this into y = 3t^2 + 2 gives y = 3((x-1)/2)^2 + 2, which simplifies to y = (3/4)x^2 - (3/2)x + (25/4). 
Thus, the corresponding x-y equation for the curve is 11eaa88b_93c6_c875_a696_a39a7c48fd09_TB5869_11.

Question 7

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5]. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Use a CAS or graphing calculator to...

Question 8

Find parametric equations describing the given curve.
The line segment from  to

Accepted Answer

The answer of Find parametric equations describing the given curve.
The...

Question 9

Which graph below corresponds to the given parametric equations? 
A) 
B) 
C) 
D)

Accepted Answer

The given parametric equations are x=cos(t) and y=sin(2t). As t increases from 0 to 2π, x takes the values of cosine function and y takes the values of sine function multiplied by 2. On observing the graphs, we can see that option C is the only graph that satisfies these conditions.

Question 10

Sketch the plane curve defined by the given parametric equations.  
A) 
B) 
C) 
D)

Accepted Answer

The answer of Sketch the plane curve defined by the...

Question 11

Sketch the plane curve defined by the given parametric equations.  
A) 
B) 
C) 
D)

Accepted Answer

The answer of Sketch the plane curve defined by the...

Question 12

Find parametric equations for the path of a projectile launched from height  ft with initial speed  ft/s at angle  from the horizontal.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find parametric equations for the path of...

Question 13

Find an x-y equation for the given parametric equations. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find an x-y equation for the given...

Question 14

Find parametric equations describing the given curve.
The circle of radius 5 centered at  , drawn counterclockwise

Accepted Answer

The answer of Find parametric equations describing the given curve.
The...

Question 15

For the given parametric equations, find a corresponding x-y equation for the curve. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of For the given parametric equations, find a...

Question 16

For the given parametric equations, find a corresponding x-y equation for the curve. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of For the given parametric equations, find a...

Question 17

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5]. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Use a CAS or graphing calculator to...

Question 18

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5]. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Use a CAS or graphing calculator to...

Question 19

For the given parametric equations, find a corresponding x-y equation for the curve. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of For the given parametric equations, find a...

Question 20

Find parametric equations for the path of a projectile launched from height  ft with initial speed  ft/s at angle  from the horizontal.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find parametric equations for the path of...

Quiz 11: Parametric Equations and Polar Coordinates

Sketch the plane curve defined by the given parametric equations.

Find parametric equations describing the given curve. The line segment from to

Find parametric equations describing the given curve. The portion of the parabola from to

Sketch the plane curve defined by the given parametric equations.

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

For the given parametric equations, find a corresponding x-y equation for the curve.

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

Find parametric equations describing the given curve. The line segment from to

Which graph below corresponds to the given parametric equations?

Sketch the plane curve defined by the given parametric equations.

Sketch the plane curve defined by the given parametric equations.

Find parametric equations for the path of a projectile launched from height ft with initial speed ft/s at angle from the horizontal.

Find an x-y equation for the given parametric equations.

Find parametric equations describing the given curve. The circle of radius 5 centered at , drawn counterclockwise

For the given parametric equations, find a corresponding x-y equation for the curve.

For the given parametric equations, find a corresponding x-y equation for the curve.

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

For the given parametric equations, find a corresponding x-y equation for the curve.

Find parametric equations for the path of a projectile launched from height ft with initial speed ft/s at angle from the horizontal.