Question 1

Determine if the given polar coordinates represent the same point.
-( 2, $\pi$/2), (-2, 3$\pi$/2)

Accepted Answer

A) True 
 B)False

Question 2

Plot the point whose polar coordinates are given.
-( -4, 0)

Accepted Answer

A)  
 
B)  
 
C)  
 
D)

Question 3

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions.
-Vertices at (0, 6) and (0, -6); foci at (0, 11) and (0, -11)

Accepted Answer

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

Question 4

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

Accepted Answer

A)  
 
B)  
 
C)  
 
D)

Question 5

Find the area of the specified region.
-Inside the lemniscate  = 6 sin 2$\theta$ and outside the circle r =

Accepted Answer

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

Question 6

Choose the equation that matches the graph.
-

Accepted Answer

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

Question 7

Graph. 
-36  + 12  = 192

Accepted Answer

A)  
 
B)  
 
C)  
 
D)

Question 8

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions.
-Vertices at ( 4, 0) and ( -4, 0); foci at ( 9, 0) and ( -9, 0)

Accepted Answer

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

Question 9

Find the focus and directrix of the parabola.
- = 8x

Accepted Answer

A)  ( 2, 0); x = 2 
B)  (0, 2); y = -2 
C)  ( 2, 0); x = -2 
D)  ( 2, 2); x = 2

Question 10

Graph the polar equation.
-r = 4(1 -sin $\theta$)

Accepted Answer

A)  
 
B)  
 
C)  
 
D)

Question 11

Graph the polar equation.
-r = 4 cos 8$\theta$

Accepted Answer

A)  
 
B)  
 
C)  
 
D)

Question 12

Find the area of the specified region.
-Inside the limacon r = 9 + 6 sin $\theta$

Accepted Answer

A)  99$\pi$ 
B)  198$\pi$- 108 
C)  99$\pi$+ 108 
D)  198$\pi$

Question 13

Find an equation of the following curve.
-A hyperbola centered at the origin having vertex at (0, -3) and eccentricity equal to 2

Accepted Answer

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

Question 14

Find the area of the specified region.
-Inside one loop of the lemniscate  = 6 cos 2$\theta$

Accepted Answer

A)  6 
B)   
C)  12 
D)  3

Question 15

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

Accepted Answer

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

Question 16

Determine if the given polar coordinates represent the same point.
-( 10, $\pi$/6), ( 10, 7$\pi$/6)

Accepted Answer

A) True 
 B)False

Question 17

Determine if the given polar coordinates represent the same point.
-( 8, $\pi$/6), (-8, 7$\pi$/6)

Accepted Answer

A) True 
 B)False

Question 18

Choose the equation that matches the graph.   
-

Accepted Answer

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

Question 19

Find the area of the specified region.
-Inside the graph of r = 3 + cos 3$\theta$

Accepted Answer

A)   
B)  19 $\pi$ 
C)   +  
D)  19 $\pi$ +

Question 20

Choose the equation that matches the graph.   
-

Accepted Answer

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

Exam 12: Parametric and Polar Curves

Determine if the given polar coordinates represent the same point. -( 2, $\pi$ /2), (-2, 3 $\pi$ /2)

Plot the point whose polar coordinates are given. -( -4, 0)

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions. -Vertices at (0, 6) and (0, -6) ; foci at (0, 11) and (0, -11)

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

Choose the equation that matches the graph. -

Graph. -36 + 12 = 192

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions. -Vertices at ( 4, 0) and ( -4, 0) ; foci at ( 9, 0) and ( -9, 0)

Find the focus and directrix of the parabola. - = 8x

Graph the polar equation. -r = 4(1 -sin $\theta$ ) $Graph the polar equation. -r = 4(1 -sin \theta ) A) B) C) D)$

Graph the polar equation. -r = 4 cos 8 $\theta$ $Graph the polar equation. -r = 4 cos 8 \theta A) B) C) D)$

Find the area of the specified region. -Inside the limacon r = 9 + 6 sin $\theta$

Find an equation of the following curve. -A hyperbola centered at the origin having vertex at (0, -3) and eccentricity equal to 2

Find the area of the specified region. -Inside one loop of the lemniscate $Find the area of the specified region. -Inside one loop of the lemniscate = 6 cos 2 \theta A) 6 B) C) 12 D) 3$ = 6 cos 2 $\theta$

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

Determine if the given polar coordinates represent the same point. -( 10, $\pi$ /6), ( 10, 7 $\pi$ /6)

Determine if the given polar coordinates represent the same point. -( 8, $\pi$ /6), (-8, 7 $\pi$ /6)

Choose the equation that matches the graph. -

Find the area of the specified region. -Inside the graph of r = 3 + cos 3 $\theta$

Choose the equation that matches the graph. -

Exam 12: Parametric and Polar Curves

Determine if the given polar coordinates represent the same point. -( 2, π\piπ /2), (-2, 3 π\piπ /2)

Plot the point whose polar coordinates are given. -( -4, 0)

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions. -Vertices at (0, 6) and (0, -6) ; foci at (0, 11) and (0, -11)

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

Find the area of the specified region. -Inside the lemniscate = 6 sin 2 θ\thetaθ and outside the circle r =

Choose the equation that matches the graph. -

Graph. -36 + 12 = 192

Find the standard-form equation of the hyperbola centered at the origin which satisfies the given conditions. -Vertices at ( 4, 0) and ( -4, 0) ; foci at ( 9, 0) and ( -9, 0)

Find the focus and directrix of the parabola. - = 8x

Graph the polar equation. -r = 4(1 -sin θ\thetaθ )

Graph the polar equation. -r = 4 cos 8 θ\thetaθ

Find the area of the specified region. -Inside the limacon r = 9 + 6 sin θ\thetaθ

Find an equation of the following curve. -A hyperbola centered at the origin having vertex at (0, -3) and eccentricity equal to 2

Find the area of the specified region. -Inside one loop of the lemniscate = 6 cos 2 θ\thetaθ

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

Determine if the given polar coordinates represent the same point. -( 10, π\piπ /6), ( 10, 7 π\piπ /6)

Determine if the given polar coordinates represent the same point. -( 8, π\piπ /6), (-8, 7 π\piπ /6)

Choose the equation that matches the graph. -

Find the area of the specified region. -Inside the graph of r = 3 + cos 3 θ\thetaθ

Choose the equation that matches the graph. -

Determine if the given polar coordinates represent the same point. -( 2, $\pi$ /2), (-2, 3 $\pi$ /2)

Graph the polar equation. -r = 4(1 -sin $\theta$ ) $Graph the polar equation. -r = 4(1 -sin \theta ) A) B) C) D)$

Graph the polar equation. -r = 4 cos 8 $\theta$ $Graph the polar equation. -r = 4 cos 8 \theta A) B) C) D)$

Find the area of the specified region. -Inside the limacon r = 9 + 6 sin $\theta$

Find the area of the specified region. -Inside one loop of the lemniscate $Find the area of the specified region. -Inside one loop of the lemniscate = 6 cos 2 \theta A) 6 B) C) 12 D) 3$ = 6 cos 2 $\theta$

Determine if the given polar coordinates represent the same point. -( 10, $\pi$ /6), ( 10, 7 $\pi$ /6)

Determine if the given polar coordinates represent the same point. -( 8, $\pi$ /6), (-8, 7 $\pi$ /6)

Find the area of the specified region. -Inside the graph of r = 3 + cos 3 $\theta$