Deck 12: Parametric Equations and Polar Coordinates

Question 1

Find a parametrization for the curve.
The line segment with endpoints (-4, -7) and ( , -15)

Answer 1

Question 2

Find an equation for the line tangent to the curve at the point defined by the given value of t.

Answer 2

A

Question 3

Graph the pair of parametric equations with the aid of a graphing calculator.

Answer 3

B

Question 4

Graph the pair of parametric equations with the aid of a graphing calculator.

Question 5

Graph the pair of parametric equations with the aid of a graphing calculator.

Question 6

Graph the pair of parametric equations with the aid of a graphing calculator.

Question 7

Parametric equations and and a parameter interval for the motion of a particle in the xy-plane are given. Identify the
particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph
traced by the particle and the direction of motion.

Question 8

Parametric equations and and a parameter interval for the motion of a particle in the xy-plane are given. Identify the
particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph
traced by the particle and the direction of motion.

Question 9

Parametric equations and and a parameter interval for the motion of a particle in the xy-plane are given. Identify the
particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph
traced by the particle and the direction of motion.

Question 10

Parametric equations and and a parameter interval for the motion of a particle in the xy-plane are given. Identify the
particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph
traced by the particle and the direction of motion.

Question 11

Find a parametrization for the curve.
The ray (half line) with initial point (-3, ) that passes through the point (-10, -3)

Question 12

Graph the pair of parametric equations with the aid of a graphing calculator.

Question 13

Graph the pair of parametric equations with the aid of a graphing calculator.

Question 14

Graph the pair of parametric equations with the aid of a graphing calculator.

Question 15

Graph the pair of parametric equations with the aid of a graphing calculator.

Question 16

Solve the problem.

Question 17

Find a parametrization for the curve.

Question 18

Graph the pair of parametric equations with the aid of a graphing calculator.

Question 19

Solve the problem.

Question 20

Graph the pair of parametric equations with the aid of a graphing calculator.

Question 21

Assuming that the equations define x and y implicitly as differentiable functions x = f(t), y = g(t), find the slope of the
curve x = f(t), y = g(t) at the given value of t.

Question 22

Assuming that the equations define x and y implicitly as differentiable functions x = f(t), y = g(t), find the slope of the
curve x = f(t), y = g(t) at the given value of t.

Question 23

Assuming that the equations define x and y implicitly as differentiable functions x = f(t), y = g(t), find the slope of the
curve x = f(t), y = g(t) at the given value of t.

A) -8
B) 2
C) 8
D) 4

Question 24

Question 25

Find an equation for the line tangent to the curve at the point defined by the given value of t.

Question 26

Find the area.
Find the area under one arch of the cycloid x = 2(t - sin t), y = 2(1 - cos t).

Question 27

Find an equation for the line tangent to the curve at the point defined by the given value of t.

Question 28

Question 29

Find an equation for the line tangent to the curve at the point defined by the given value of t.

Question 30

Find an equation for the line tangent to the curve at the point defined by the given value of t.

Question 31

Assuming that the equations define x and y implicitly as differentiable functions x = f(t), y = g(t), find the slope of the
curve x = f(t), y = g(t) at the given value of t.

Question 32

Question 33

Find an equation for the line tangent to the curve at the point defined by the given value of t.

Question 34

Question 35

Question 36

Question 37

Assuming that the equations define x and y implicitly as differentiable functions x = f(t), y = g(t), find the slope of the
curve x = f(t), y = g(t) at the given value of t.

A) - 6
B) 9
C) - 9
D) - 4

Question 38

Assuming that the equations define x and y implicitly as differentiable functions x = f(t), y = g(t), find the slope of the
curve x = f(t), y = g(t) at the given value of t.

Question 39

A) 14
B) -14
C) 0
D) -7

Question 40

Question 41

Find the length of the curve.

Question 42

Find the length of the curve.

A) 7
B) 42
C) 14
D) 21

Question 43

Find the area.

Question 44

Find the length of the curve.

Question 45

Find the area of the surface generated by revolving the curves about the indicated axis.

Question 46

Find the length of the curve.

Question 47

Determine if the given polar coordinates represent the same point.

A) Yes
B) No

Question 48

Find the length of the curve.

Question 49

Find the length of the curve.

Question 50

Find the area of the surface generated by revolving the curves about the indicated axis.

Question 51

Find the length of the curve.

Question 52

Find the area.

A) 4
B) 9
C) 8
D) 5

Question 53

Find the length of the curve.

Question 54

Find the coordinates of the centroid of the curve.

Question 55

Determine if the given polar coordinates represent the same point.

A) No
B) Yes

Question 56

Determine if the given polar coordinates represent the same point.

A) Yes
B) No

Question 57

Find the coordinates of the centroid of the curve.

Question 58

Find the length of the curve.

Question 59

Determine if the given polar coordinates represent the same point.

A) Yes
B) No

Question 60

Find the length of the curve.

Question 61

Plot the point whose polar coordinates are given.

Question 62

Find the Cartesian coordinates of the given point.

Question 63

Determine if the given polar coordinates represent the same point.

A) Yes
B) No

Question 64

Find the Cartesian coordinates of the given point.

A) (-3, 0)
B) (0, -3)
C) (3, 0)
D) (0, 3)

Question 65

Find all the polar coordinates of the point.

Question 66

Find the Cartesian coordinates of the given point.

Question 67

Find the Cartesian coordinates of the given point.

Question 68

Determine if the given polar coordinates represent the same point.

A) No
B) Yes

Question 69

Find all the polar coordinates of the point.

Question 70

Find the Cartesian coordinates of the given point.

Question 71

Determine if the given polar coordinates represent the same point.

A) No
B) Yes

Question 72

Determine if the given polar coordinates represent the same point.

A) Yes
B) No

Question 73

Plot the point whose polar coordinates are given.

Question 74

Find the Cartesian coordinates of the given point.
( , 0)

A) (0, 7)
B) (0, -7)
C) (-7, 0)
D) (7, 0)

Question 75

Plot the point whose polar coordinates are given.

Question 76

Find the Cartesian coordinates of the given point.

A) (0, -9)
B) (-9, 0)
C) (9, 0)
D) (0, 9)

Question 77

Find the Cartesian coordinates of the given point.

Question 78

Determine if the given polar coordinates represent the same point.

A) No
B) Yes

Question 79

Find the Cartesian coordinates of the given point.

Question 80

Describe the graph of the polar equation.

A) Vertical line through (-11, 0)
B) Line through origin with slope -11
C) Circle of radius 11 centered at origin
D) Horizontal line through (0, -11)