Question 1

Solve the problem.  
-Find the vertices and asymptotes of the following hyperbola:   -   = 1

Accepted Answer

A)  Vertices: (0, 16), (0, -16); Asymptotes: y = ±   x 
B)  Vertices: (0, 4), (0, -4); Asymptotes: y = ± 4x 
C)  Vertices: (0, 4), (0, -4); Asymptotes: y = ±   x 
D)  Vertices: (4, 0), (-4, 0); Asymptotes: y = ±   x 
A)  Vertices: (0, 16), (0, -16); Asymptotes: y = ±   x 
B)  Vertices: (0, 4), (0, -4); Asymptotes: y = ± 4x 
C)  Vertices: (0, 4), (0, -4); Asymptotes: y = ±   x 
D)  Vertices: (4, 0), (-4, 0); Asymptotes: y = ±   x C

Question 2

Solve the problem.  
-Find the foci and asymptotes of the following hyperbola: 4   - 25   = 100

Accepted Answer

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

Question 3

Graph the parabola.
-x = 4y2

Accepted Answer

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

Question 4

Graph the polar equation.
-  = 60 cos 3$\theta$

Accepted Answer

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

Question 5

Graph the polar equation.
-  = 18 sin 3$\theta$

Accepted Answer

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

Question 6

Find the Cartesian coordinates of the given point.
-( -5, $\pi$)

Accepted Answer

A)  ( 0, 5) 
B)  (-5, 0) 
C)  (5, 0) 
D)  ( 0, -5) 
A)  ( 0, 5) 
B)  (-5, 0) 
C)  (5, 0) 
D)  ( 0, -5)

Question 7

Choose the equation that matches the graph.   
-

Accepted Answer

A)    -   = 1 
B)    +   = 1 
C)    +   = 1 
D)    +   = 1 
A)    -   = 1 
B)    +   = 1 
C)    +   = 1 
D)    +   = 1

Question 8

Find the standard-form equation of the ellipse centered at the origin and satisfying the given conditions.
-An ellipse with length of major axis 14 and y-intercepts

Accepted Answer

A)    +   = 1 
B)    +   = 1 
C)    +   = 1 
D)    +   = 1 
A)    +   = 1 
B)    +   = 1 
C)    +   = 1 
D)    +   = 1

Question 9

Find the length of the curve.
-The spiral r =   , 0 $\le$ $\theta$ $\le$ 2

Accepted Answer

A)  56 
B)      
C)  8((   + )   -1 ) 
D)      
A)  56 
B)      
C)  8((   + )   -1 ) 
D)

Question 10

Find the area of the specified region.
-Inside one leaf of the four-leaved rose r = 7 sin 2$\theta$

Accepted Answer

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

Question 11

Find the Cartesian coordinates of the given point.
-(-4, -$\pi$/3)

Accepted Answer

A)  (-2   , 2 ) 
B) (2, 2   ) 
C)  (-2 , 2   ) 
D)  (-2   , -2) 
A)  (-2   , 2 ) 
B) (2, 2   ) 
C)  (-2 , 2   ) 
D)  (-2   , -2)

Question 12

Graph the parabola or ellipse. Include the directrix that corresponds to the focus at the origin.
-r =

Accepted Answer

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

Question 13

Determine if the given polar coordinates represent the same point.
-(r, $\theta$), (-r, $\theta$ + $\pi$)

Accepted Answer

A) True 
 B)False

Question 14

Find the focus and directrix of the parabola.
-  = -32x

Accepted Answer

A)  ( -8, 0); x = 8 
B)  (0, -8); y = 8 
C)  ( -8, 0); y = 8 
D)  ( 8, 0); x = -8 
A)  ( -8, 0); x = 8 
B)  (0, -8); y = 8 
C)  ( -8, 0); y = 8 
D)  ( 8, 0); x = -8

Question 15

Determine if the given polar coordinates represent the same point.
-( 2, $\pi$/4), (-2, $\pi$/4)

Accepted Answer

A) True 
 B)False

Question 16

Graph. 
-9   + 6   = 18

Accepted Answer

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

Question 17

Find the length of the curve.
-The spiral r =   , 0 $\le$ $\theta$ $\le$  $\pi$

Accepted Answer

A)    (   - 1) 
B)    (   - 1) 
C)    (   - 1) 
D)    -   
A)    (   - 1) 
B)    (   - 1) 
C)    (   - 1) 
D)    -

Question 18

Replace the polar equation with an equivalent Cartesian equation.
-  + 2   sin$\theta$cos$\theta$= 625

Accepted Answer

A)    + 3   = 625 
B)  x + y =25 
C)    +   = 625 
D)  x + y = ±25 
A)    + 3   = 625 
B)  x + y =25 
C)    +   = 625 
D)  x + y = ±25

Question 19

Find the area of the specified region.
-Inside the circle r = a sin$\theta$ and outside the cardioid r = a(1 - sin $\theta$), a > 0

Accepted Answer

A)    (4 $\pi$ - 3   ) 
B)    (6 - $\pi$) 
C)    (2 $\pi$ - 3   ) 
D)    (3   - $\pi$ ) 
A)    (4 $\pi$ - 3   ) 
B)    (6 - $\pi$) 
C)    (2 $\pi$ - 3   ) 
D)    (3   - $\pi$ )

Question 20

Graph the pair of parametric equations with the aid of a graphing calculator.
-x = 5 cos 2t + 4 cos 6t, y = 5 sin 2t - 4 sin 6t, 0 $\le$ t $\le$$\pi$

Accepted Answer

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

Solve the problem. -Find the vertices and asymptotes of the following hyperbola: - = 1

Solve the problem. -Find the foci and asymptotes of the following hyperbola: 4 - 25 = 100

Graph the parabola. -x = 4y²

Graph the polar equation. - $Graph the polar equation. - = 60 cos 3 \theta$ = 60 cos 3 $\theta$ $Graph the polar equation. - = 60 cos 3 \theta$

Graph the polar equation. - $Graph the polar equation. - = 18 sin 3 \theta$ = 18 sin 3 $\theta$ $Graph the polar equation. - = 18 sin 3 \theta$

Find the Cartesian coordinates of the given point. -( -5, $\pi$ )

Choose the equation that matches the graph. -

Find the standard-form equation of the ellipse centered at the origin and satisfying the given conditions. -An ellipse with length of major axis 14 and y-intercepts

Find the length of the curve. -The spiral r = $Find the length of the curve. -The spiral r = , 0 \le \theta \le 2$ , 0 $\le$ $\theta$ $\le$ 2 $Find the length of the curve. -The spiral r = , 0 \le \theta \le 2$

Find the area of the specified region. -Inside one leaf of the four-leaved rose r = 7 sin 2 $\theta$

Find the Cartesian coordinates of the given point. -(-4, - $\pi$ /3)

Graph the parabola or ellipse. Include the directrix that corresponds to the focus at the origin. -r =

Determine if the given polar coordinates represent the same point. -(r, $\theta$ ), (-r, $\theta$ + $\pi$ )

Find the focus and directrix of the parabola. - = -32x

Determine if the given polar coordinates represent the same point. -( 2, $\pi$ /4), (-2, $\pi$ /4)

Graph. -9 + 6 = 18

Find the length of the curve. -The spiral r = $Find the length of the curve. -The spiral r = , 0 \le \theta \le \pi$ , 0 $\le$ $\theta$ $\le$ $\pi$

Find the area of the specified region. -Inside the circle r = a sin $\theta$ and outside the cardioid r = a(1 - sin $\theta$ ), a > 0

Graph the pair of parametric equations with the aid of a graphing calculator. -x = 5 cos 2t + 4 cos 6t, y = 5 sin 2t - 4 sin 6t, 0 $\le$ t $\le$ $\pi$ $Graph the pair of parametric equations with the aid of a graphing calculator. -x = 5 cos 2t + 4 cos 6t, y = 5 sin 2t - 4 sin 6t, 0 \le t \le\pi$

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Exam 12: Parametric and Polar Curves

Solve the problem. -Find the vertices and asymptotes of the following hyperbola: - = 1

Solve the problem. -Find the foci and asymptotes of the following hyperbola: 4 - 25 = 100

Graph the parabola. -x = 4y2

Graph the polar equation. - = 60 cos 3 θ\thetaθ

Graph the polar equation. - = 18 sin 3 θ\thetaθ

Find the Cartesian coordinates of the given point. -( -5, π\piπ )

Choose the equation that matches the graph. -

Find the standard-form equation of the ellipse centered at the origin and satisfying the given conditions. -An ellipse with length of major axis 14 and y-intercepts

Find the length of the curve. -The spiral r = , 0 ≤\le≤ θ\thetaθ ≤\le≤ 2

Find the area of the specified region. -Inside one leaf of the four-leaved rose r = 7 sin 2 θ\thetaθ

Find the Cartesian coordinates of the given point. -(-4, - π\piπ /3)

Graph the parabola or ellipse. Include the directrix that corresponds to the focus at the origin. -r =

Determine if the given polar coordinates represent the same point. -(r, θ\thetaθ ), (-r, θ\thetaθ + π\piπ )

Find the focus and directrix of the parabola. - = -32x

Determine if the given polar coordinates represent the same point. -( 2, π\piπ /4), (-2, π\piπ /4)

Graph. -9 + 6 = 18

Find the length of the curve. -The spiral r = , 0 ≤\le≤ θ\thetaθ ≤\le≤ π\piπ

Replace the polar equation with an equivalent Cartesian equation. - + 2 sin θ\thetaθ cos θ\thetaθ = 625

Find the area of the specified region. -Inside the circle r = a sin θ\thetaθ and outside the cardioid r = a(1 - sin θ\thetaθ ), a > 0

Graph the pair of parametric equations with the aid of a graphing calculator. -x = 5 cos 2t + 4 cos 6t, y = 5 sin 2t - 4 sin 6t, 0 ≤\le≤ t ≤\le≤π\piπ

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Graph the parabola. -x = 4y²

Graph the polar equation. - $Graph the polar equation. - = 60 cos 3 \theta$ = 60 cos 3 $\theta$ $Graph the polar equation. - = 60 cos 3 \theta$

Graph the polar equation. - $Graph the polar equation. - = 18 sin 3 \theta$ = 18 sin 3 $\theta$ $Graph the polar equation. - = 18 sin 3 \theta$

Find the Cartesian coordinates of the given point. -( -5, $\pi$ )

Find the length of the curve. -The spiral r = $Find the length of the curve. -The spiral r = , 0 \le \theta \le 2$ , 0 $\le$ $\theta$ $\le$ 2 $Find the length of the curve. -The spiral r = , 0 \le \theta \le 2$

Find the area of the specified region. -Inside one leaf of the four-leaved rose r = 7 sin 2 $\theta$

Find the Cartesian coordinates of the given point. -(-4, - $\pi$ /3)

Determine if the given polar coordinates represent the same point. -(r, $\theta$ ), (-r, $\theta$ + $\pi$ )

Determine if the given polar coordinates represent the same point. -( 2, $\pi$ /4), (-2, $\pi$ /4)

Find the length of the curve. -The spiral r = $Find the length of the curve. -The spiral r = , 0 \le \theta \le \pi$ , 0 $\le$ $\theta$ $\le$ $\pi$

Find the area of the specified region. -Inside the circle r = a sin $\theta$ and outside the cardioid r = a(1 - sin $\theta$ ), a > 0

Graph the pair of parametric equations with the aid of a graphing calculator. -x = 5 cos 2t + 4 cos 6t, y = 5 sin 2t - 4 sin 6t, 0 $\le$ t $\le$ $\pi$ $Graph the pair of parametric equations with the aid of a graphing calculator. -x = 5 cos 2t + 4 cos 6t, y = 5 sin 2t - 4 sin 6t, 0 \le t \le\pi$