Question 1

Find all points of intersection of the two curves.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 2

Which graph below corresponds to the given parametric equations?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 3

At time t = 0 seconds, a hockey puck is headed towards the "board" (the wall around the perimeter of the area of play) as shown in the figure (the view is from above the playing surface). At that same instant, a hockey player at a different position on the ice is headed straight up the ice in order to intercept the puck (see figure). The trajectories of the puck and the player are described by the following set of parametric equations:   Find the location(s) of intersection of the trajectories of the player and the puck. Distances are in feet and time is in seconds.   [figure is not necessarily drawn to scale]

Accepted Answer

A)    and   
B)    
C)    and   
D)    
A)    and   
B)    
C)    and   
D)

Question 4

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix y = -2, e = 2

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 5

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

Accepted Answer

Answers ma

Question 6

Compute the surface area of the surface obtained by revolving the given curve about the indicated axis.

Accepted Answer

A)  237.13 
B)  470.92 
C)  840.14 
D)  34.55 
A)  237.13 
B)  470.92 
C)  840.14 
D)  34.55

Question 7

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

Accepted Answer

Answers ma

Question 8

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

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 9

Find an equation for the indicated conic section. Hyperbola with foci (-1, 18), (-1, -16) and vertices (-1, 16), (-1, -14)

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 10

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

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 11

Find a polar equation corresponding to the given rectangular equation. x = 1

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 12

Plot the given polar point.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 13

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

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 14

Identify all points at which the curve has a vertical tangent.

Accepted Answer

A)    
B)  (1,0) 
C)    
D)    
A)    
B)  (1,0) 
C)    
D)

Question 15

Identify all values of   where r = 0.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 16

Find all polar coordinate representations of the given rectangular point.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

Find the vertices, foci, and directrices of the given ellipse.

Accepted Answer

A)  vertices   ; foci (2, -4), (-8, -4); directrices   
B)  vertices   ; foci (2, -4), (-8, -4); directrices   
C)  vertices (2, -4), (-8, -4); foci   ; directrices   
D)  vertices (2, -4), (-8, -4); foci   ; directrices   
A)  vertices   ; foci (2, -4), (-8, -4); directrices   
B)  vertices   ; foci (2, -4), (-8, -4); directrices   
C)  vertices (2, -4), (-8, -4); foci   ; directrices   
D)  vertices (2, -4), (-8, -4); foci   ; directrices

Question 18

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

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 19

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

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 20

Sketch the plane curve defined by the given parametric equations.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Find all points of intersection of the two curves.

Which graph below corresponds to the given parametric equations?

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix y = -2, e = 2

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

Compute the surface area of the surface obtained by revolving the given curve about the indicated axis.

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

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 equation for the indicated conic section. Hyperbola with foci (-1, 18), (-1, -16) and vertices (-1, 16), (-1, -14)

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

Find a polar equation corresponding to the given rectangular equation. x = 1

Plot the given polar point.

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

Identify all points at which the curve has a vertical tangent.

Identify all values of where r = 0.

Find all polar coordinate representations of the given rectangular point.

Find the vertices, foci, and directrices of the given ellipse.

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

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

Sketch the plane curve defined by the given parametric equations.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 11: Parametric Equations and Polar Coordinates

Find all points of intersection of the two curves.

Which graph below corresponds to the given parametric equations?

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix y = -2, e = 2

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

Compute the surface area of the surface obtained by revolving the given curve about the indicated axis.

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

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 equation for the indicated conic section. Hyperbola with foci (-1, 18), (-1, -16) and vertices (-1, 16), (-1, -14)

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

Find a polar equation corresponding to the given rectangular equation. x = 1

Plot the given polar point.

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

Identify all points at which the curve has a vertical tangent.

Identify all values of where r = 0.

Find all polar coordinate representations of the given rectangular point.

Find the vertices, foci, and directrices of the given ellipse.

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

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

Sketch the plane curve defined by the given parametric equations.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters