Question 1

Find the area of the specified region.
-Inside the cardioid r = $\alpha$(1 + sin $\theta$), $\alpha$ > 0

Accepted Answer

A)    - 2   
B)    
C)    + 2   
D)  2$\alpha$ $\pi$ 
A)    - 2   
B)    
C)    + 2   
D)  2$\alpha$ $\pi$

Question 2

Find the length of the curve.
-The circle r = 7 cos $\theta$

Accepted Answer

A)    $\pi$ 
B)  14 $\pi$ 
C)  7 $\pi$ 
D)  49 $\pi$ 
A)    $\pi$ 
B)  14 $\pi$ 
C)  7 $\pi$ 
D)  49 $\pi$

Question 3

Find the area of the specified region.
-Inside the six-leaved rose   = 8 cos 3$\theta$

Accepted Answer

A)  4 
B)  8 
C)  16 
D)    
A)  4 
B)  8 
C)  16 
D)

Question 4

Find a parametrization for the curve.
-The line segment with endpoints ( -8, -7) and ( 0, -12)

Accepted Answer

Answers will vary. P

Question 5

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

Accepted Answer

A)    (5  $\pi$ - 8) 
B)    (2 $\pi$ - 3   ) 
C)    (3   -  $\pi$ ) 
D)    (5  $\pi$ - 9   ) 
A)    (5  $\pi$ - 8) 
B)    (2 $\pi$ - 3   ) 
C)    (3   -  $\pi$ ) 
D)    (5  $\pi$ - 9   )

Question 6

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions.
-Foci at ( 0, -10), ( 0, 10); asymptotes: y =   x, y = -   x

Accepted Answer

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

Question 7

Calculate the arc length of the indicated portion of the curve r(t).
-r(t) = ( 7   2t)j + ( 7   2t)k;    $\pi$ $\le$ t $\le$   $\pi$

Accepted Answer

A)  0 
B)    
C)    
D)  21 
A)  0 
B)    
C)    
D)  21

Question 8

Find the Cartesian coordinates of the given point.
-

Accepted Answer

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

Question 9

Find a parametrization for the curve.
-The upper half of the parabola x + 3 =

Accepted Answer

Answers will vary. P

Question 10

Find the focus and directrix of the parabola.
-  - 16x = 0

Accepted Answer

A)  ( 4, 0); y = -4 
B)  ( 4, 0); x = -4 
C)  (0, 4); y = -4 
D)  ( 4, 0); x = 4 
A)  ( 4, 0); y = -4 
B)  ( 4, 0); x = -4 
C)  (0, 4); y = -4 
D)  ( 4, 0); x = 4

Question 11

Replace the polar equation with an equivalent Cartesian equation.
-r cos $\theta$ = 13

Accepted Answer

A)  13y = 1 
B)  x = 13 
C)  y = 13 
D)  13x = 1 
A)  13y = 1 
B)  x = 13 
C)  y = 13 
D)  13x = 1

Question 12

Find the standard-form equation of the ellipse centered at the origin and satisfying the given conditions.
-An ellipse with intercepts (±2, 0) and (0, ±5)

Accepted Answer

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

Question 13

Find the standard-form equation of the ellipse centered at the origin and satisfying the given conditions.
-An ellipse with vertices (0, ±8) and foci (0, ±4)

Accepted Answer

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

Question 14

Find the area of the specified region.
-Inside the circle r = 7 and to the right of the line r =   sec $\theta$

Accepted Answer

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

Question 15

Find the area of the specified region.
-Inside the three-leaved rose r = 6 cos 3$\theta$

Accepted Answer

A)    $\pi$ 
B)  3$\pi$ 
C)  18$\pi$ 
D)  9$\pi$ 
A)    $\pi$ 
B)  3$\pi$ 
C)  18$\pi$ 
D)  9$\pi$

Question 16

Find the focus and directrix of the parabola.
-y = 3

Accepted Answer

A)    , y = -   
B)    , x = -   
C)    , y =   
D)    , x = -   
A)    , y = -   
B)    , x = -   
C)    , y =   
D)    , x = -

Question 17

Find the vertices and foci of the ellipse.
-  +   = 1

Accepted Answer

A)  Vertices: (±25, 0); Foci: (±15, 0) 
B)  Vertices: (0, ±25); Foci: (0, ±20) 
C)  Vertices: (±25, 0); Foci: (±20, 0) 
D)  Vertices: (0, ±25); Foci: (0, ±15) 
A)  Vertices: (±25, 0); Foci: (±15, 0) 
B)  Vertices: (0, ±25); Foci: (0, ±20) 
C)  Vertices: (±25, 0); Foci: (±20, 0) 
D)  Vertices: (0, ±25); Foci: (0, ±15)

Question 18

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 19

Find the vertices and foci of the ellipse.
-36   + 49   = 1764

Accepted Answer

A)  Vertices: (±7, 0); Foci: (±   , 0) 
B)  Vertices: (0, ±7); Foci (0, ±   ) 
C)  Vertices: (±6, 0); Foci: (±   , 0) 
D)  Vertices: (0, ±6); Foci (0, ±   ) 
A)  Vertices: (±7, 0); Foci: (±   , 0) 
B)  Vertices: (0, ±7); Foci (0, ±   ) 
C)  Vertices: (±6, 0); Foci: (±   , 0) 
D)  Vertices: (0, ±6); Foci (0, ±   )

Question 20

Choose the equation that matches the graph.
-

Accepted Answer

A)    = 4y 
B)  4   = y 
C)    = -4y 
D)    = 4x 
A)    = 4y 
B)  4   = y 
C)    = -4y 
D)    = 4x

Find the area of the specified region. -Inside the cardioid r = $\alpha$ (1 + sin $\theta$ ), $\alpha$ > 0

Find the length of the curve. -The circle r = 7 cos $\theta$

Find the area of the specified region. -Inside the six-leaved rose $Find the area of the specified region. -Inside the six-leaved rose = 8 cos 3 \theta$ = 8 cos 3 $\theta$

Find a parametrization for the curve. -The line segment with endpoints ( -8, -7) and ( 0, -12)

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

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions. -Foci at ( 0, -10), ( 0, 10); asymptotes: y = x, y = - x

Find the Cartesian coordinates of the given point. -

Find a parametrization for the curve. -The upper half of the parabola x + 3 =

Find the focus and directrix of the parabola. - - 16x = 0

Replace the polar equation with an equivalent Cartesian equation. -r cos $\theta$ = 13

Find the standard-form equation of the ellipse centered at the origin and satisfying the given conditions. -An ellipse with intercepts (±2, 0) and (0, ±5)

Find the standard-form equation of the ellipse centered at the origin and satisfying the given conditions. -An ellipse with vertices (0, ±8) and foci (0, ±4)

Find the area of the specified region. -Inside the circle r = 7 and to the right of the line r = $Find the area of the specified region. -Inside the circle r = 7 and to the right of the line r = sec \theta$ sec $\theta$

Find the area of the specified region. -Inside the three-leaved rose r = 6 cos 3 $\theta$

Find the focus and directrix of the parabola. -y = 3

Find the vertices and foci of the ellipse. - + = 1

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

Find the vertices and foci of the ellipse. -36 + 49 = 1764

Choose the equation that matches the graph. -

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Exam 12: Parametric and Polar Curves

Find the area of the specified region. -Inside the cardioid r = α\alphaα (1 + sin θ\thetaθ ), α\alphaα > 0

Find the length of the curve. -The circle r = 7 cos θ\thetaθ

Find the area of the specified region. -Inside the six-leaved rose = 8 cos 3 θ\thetaθ