Question 1

Find the slope of the line with inclination $\theta$ . Round your answer to four decimal places. $\theta = 2.26 \text { radians }$

Accepted Answer

A)  $m \approx - 1.6136$ 
B)  $m \approx - 1.4136$ 
C)  $m \approx - 1.2136$ 
D)  $m \approx - 1.5136$ 
E)  $m \approx - 1.3136$ 
A)  $m \approx - 1.6136$ 
B)  $m \approx - 1.4136$ 
C)  $m \approx - 1.2136$ 
D)  $m \approx - 1.5136$ 
E)  $m \approx - 1.3136$ C

Question 2

Find the center and vertices of the ellipse. $$\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 4 } = 1$$

Accepted Answer

A)  center: $( 7,2 ) \quad$ vertices: $( - 7 , - 2 ) , ( 7,2 )$ 
B)  center: $( 0,0 ) \quad$ vertices: $( 0 , - 7 ) , ( 0,7 )$ 
C)  center: $( 0,0 ) \quad$ vertices: $( - 7,0 ) , ( 7,0 )$ 
D)  center: $( 7,0 ) \quad$ vertices: $( 0 , - 2 ) , ( 0,2 )$ 
E)  center: $( 0,0 ) \quad$ vertices: $( - 2,0 ) , ( 2,0 )$ 
A)  center: $( 7,2 ) \quad$ vertices: $( - 7 , - 2 ) , ( 7,2 )$ 
B)  center: $( 0,0 ) \quad$ vertices: $( 0 , - 7 ) , ( 0,7 )$ 
C)  center: $( 0,0 ) \quad$ vertices: $( - 7,0 ) , ( 7,0 )$ 
D)  center: $( 7,0 ) \quad$ vertices: $( 0 , - 2 ) , ( 0,2 )$ 
E)  center: $( 0,0 ) \quad$ vertices: $( - 2,0 ) , ( 2,0 )$ C

Question 3

Convert the rectangular equation to polar form. Assume 
$a > 0$ 
$x y = 10$

Accepted Answer

A)  $r ^ { 2 } = 10 \sec 2 \theta$ 
B)  $r ^ { 2 } = 20 \csc 2 \theta$ 
C)  $r ^ { 2 } = 20 \sec 2 \theta$ 
D)  $r ^ { 2 } = 10 \csc 2 \theta$ 
E)  $r ^ { 2 } = 20 \cos 2 \theta$ 
A)  $r ^ { 2 } = 10 \sec 2 \theta$ 
B)  $r ^ { 2 } = 20 \csc 2 \theta$ 
C)  $r ^ { 2 } = 20 \sec 2 \theta$ 
D)  $r ^ { 2 } = 10 \csc 2 \theta$ 
E)  $r ^ { 2 } = 20 \cos 2 \theta$ B

Question 4

Find the standard form of the equation of the parabola with the given characteristics. $\text { Vertex: } ( 1,3 ) \text {; directrix: } y = - 2$

Accepted Answer

A)  $( x - 1 ) ^ { 2 } = 3 ( y - 3 )$ 
B)  $( x - 1 ) ^ { 2 } = 20 ( y - 3 )$ 
C)  $( y - 1 ) ^ { 2 } = 3 ( x - 3 )$ 
D)  $( x - 1 ) ^ { 2 } = - 20 ( y - 3 )$ 
E)  $( y - 1 ) ^ { 2 } = - 20 ( x - 3 )$ 
A)  $( x - 1 ) ^ { 2 } = 3 ( y - 3 )$ 
B)  $( x - 1 ) ^ { 2 } = 20 ( y - 3 )$ 
C)  $( y - 1 ) ^ { 2 } = 3 ( x - 3 )$ 
D)  $( x - 1 ) ^ { 2 } = - 20 ( y - 3 )$ 
E)  $( y - 1 ) ^ { 2 } = - 20 ( x - 3 )$

Question 5

Select the polar equation with graph.

Accepted Answer

A)  $\frac { 3 } { 1 - 2 \sin \theta }$ 
B)  $\frac { 1 } { 1 - 2 \sin \theta }$ 
C)  $\frac { 3 } { 1 + 2 \cos \theta }$ 
D)  $\frac { 3 } { 1 + 2 \sin \theta }$ 
E)  $\frac { 3 } { 1 - 2 \cos \theta }$ 
A)  $\frac { 3 } { 1 - 2 \sin \theta }$ 
B)  $\frac { 1 } { 1 - 2 \sin \theta }$ 
C)  $\frac { 3 } { 1 + 2 \cos \theta }$ 
D)  $\frac { 3 } { 1 + 2 \sin \theta }$ 
E)  $\frac { 3 } { 1 - 2 \cos \theta }$

Question 6

Find the center, vertices and foci of the hyperbola. $$\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 64 } = 1$$

Accepted Answer

A)  Center: $( 64,81 )$
Vertices: $( \pm 8,0 )$
Foci: $( \pm \sqrt { 145 } , 0 )$ 
B)  Center: $( 0,0 )$
Vertices: $( 0 , \pm 8 )$
Foci: $( 0 , \pm \sqrt { 145 } )$ 
C)  Center: $( 0,0 )$
Vertices: $( \pm 8,0 )$
Foci: $( \pm \sqrt { 145 } , 0 )$ 
D)  Center: $( 64,81 )$
Vertices: $( \pm 9,0 )$
Foci: $( \pm \sqrt { 145 } , 0 )$ 
E)  Center: $( 0,0 )$
Vertices: $( \pm 9,0 )$
Foci: $( \pm \sqrt { 145 } , 0 )$ 
A)  Center: $( 64,81 )$
Vertices: $( \pm 8,0 )$
Foci: $( \pm \sqrt { 145 } , 0 )$ 
B)  Center: $( 0,0 )$
Vertices: $( 0 , \pm 8 )$
Foci: $( 0 , \pm \sqrt { 145 } )$ 
C)  Center: $( 0,0 )$
Vertices: $( \pm 8,0 )$
Foci: $( \pm \sqrt { 145 } , 0 )$ 
D)  Center: $( 64,81 )$
Vertices: $( \pm 9,0 )$
Foci: $( \pm \sqrt { 145 } , 0 )$ 
E)  Center: $( 0,0 )$
Vertices: $( \pm 9,0 )$
Foci: $( \pm \sqrt { 145 } , 0 )$

Question 7

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. 
$\text { Vertices: } ( \pm 5,0 ) \text {; asymptotes: } y = \pm 9 x$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 2025 } = 1$ 
B) $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 2025 } = 1$ 
C)  $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 2025 } = 1$ 
D)  $\frac { y ^ { 2 } } { 2025 } - \frac { x ^ { 2 } } { 25 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 2025 } = 1$ 
A)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 2025 } = 1$ 
B) $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 2025 } = 1$ 
C)  $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 2025 } = 1$ 
D)  $\frac { y ^ { 2 } } { 2025 } - \frac { x ^ { 2 } } { 25 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 2025 } = 1$

Question 8

Find the slope of the line with inclination $\theta$ . Round your answer to four decimal places. $\theta = 2.88 \text { radians }$

Accepted Answer

A)  $m \approx - 0.4677$ 
B)  $m \approx - 0.5677$ 
C)  $m \approx - 0.3677$ 
D)  $m \approx - 0.2677$ 
E)  $m \approx - 0.6677$ 
A)  $m \approx - 0.4677$ 
B)  $m \approx - 0.5677$ 
C)  $m \approx - 0.3677$ 
D)  $m \approx - 0.2677$ 
E)  $m \approx - 0.6677$

Question 9

Consider a line with slope m and y-intercept $( 0,8 )$ Write the distance d between the point $( 7,1 )$ and the line as a function of m.

Accepted Answer

A)  $\frac { 7 | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
B)  $\frac { | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
C)  $\frac { 7 | m - 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
D)  $\frac { 7 | m + 1 | } { \sqrt { m ^ { 2 } - 1 } }$ 
E)  $\frac { 7 | m + 7 | } { \sqrt { m ^ { 2 } + 1 } }$ 
A)  $\frac { 7 | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
B)  $\frac { | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
C)  $\frac { 7 | m - 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
D)  $\frac { 7 | m + 1 | } { \sqrt { m ^ { 2 } - 1 } }$ 
E)  $\frac { 7 | m + 7 | } { \sqrt { m ^ { 2 } + 1 } }$

Question 10

Identify the conic as a circle or an ellipse then find the radius. 
$\frac { x ^ { 2 } } { 36 / 49 } + \frac { ( y + 1 ) ^ { 2 } } { 36 / 49 } = 1$

Accepted Answer

A)  Ellipse
Center: $\frac { 6 } { 7 }$ 
B)  Circle
Radius: $\frac { 6 } { 7 }$ 
C)  Circle
Radius: 1 
D)  Ellipse
Center: 1 
E)  None of the above 
A)  Ellipse
Center: $\frac { 6 } { 7 }$ 
B)  Circle
Radius: $\frac { 6 } { 7 }$ 
C)  Circle
Radius: 1 
D)  Ellipse
Center: 1 
E)  None of the above

Question 11

Consider a line with slope m and y-intercept $( 0,6 )$ Select the graph of the distance between the origin and the line.

Accepted Answer

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

Question 12

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. 
$\begin{array} { l } 
x = 5 \sin 2 \theta \
y = 5 \cos 2 \theta
\end{array}$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 25 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 2 } = 1$ 
D)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 2 } = 0$ 
E) $y = \frac { x } { 2 }$ 
A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 25 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 2 } = 1$ 
D)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 2 } = 0$ 
E) $y = \frac { x } { 2 }$

Question 13

Select the curve represented by the parametric equations. $\text { Prolate cycloid: } x = \theta - \frac { 5 } { 4 } \sin \theta , y = 1 - \frac { 5 } { 4 } \cos \theta$

Accepted Answer

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

Question 14

Give the standard form of the equation of the parabola with the given characteristics.

Accepted Answer

A)  $( x - 1 ) ^ { 2 } = - 20 ( y - 3 )$ 
B)  $( y - 3 ) ^ { 2 } = - 20 ( x - 1 )$ 
C)  $( y + 3 ) ^ { 2 } = 20 ( x + 1 )$ 
D)  $( y - 3 ) ^ { 2 } = 20 ( x - 1 )$ 
E)  $( x + 1 ) ^ { 2 } = - 20 ( y + 3 )$ 
A)  $( x - 1 ) ^ { 2 } = - 20 ( y - 3 )$ 
B)  $( y - 3 ) ^ { 2 } = - 20 ( x - 1 )$ 
C)  $( y + 3 ) ^ { 2 } = 20 ( x + 1 )$ 
D)  $( y - 3 ) ^ { 2 } = 20 ( x - 1 )$ 
E)  $( x + 1 ) ^ { 2 } = - 20 ( y + 3 )$

Question 15

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = - 3$

Accepted Answer

A)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$,polar axis, pole  Circle with radius 3
  
B)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$, polar axis, pole Circle with radius 3
  
C)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$, polar axis, pole Circle with radius 3
  
D) 
Symmetric with respect to $\theta = \frac { \pi } { 2 }$, polar axis, pole 
Circle with radius 3
  
E)  $\quad$ Symmetric with respect to $\theta = \frac { \pi } { 2 }$, polar axis, pole 
Circle with radius 3 
  
A)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$,polar axis, pole  Circle with radius 3
  
B)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$, polar axis, pole Circle with radius 3
  
C)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$, polar axis, pole Circle with radius 3
  
D) 
Symmetric with respect to $\theta = \frac { \pi } { 2 }$, polar axis, pole 
Circle with radius 3
  
E)  $\quad$ Symmetric with respect to $\theta = \frac { \pi } { 2 }$, polar axis, pole 
Circle with radius 3

Question 16

Find the vertex and focus of the parabola. $$y ^ { 2 } = \frac { 7 } { 9 } x$$

Accepted Answer

A)  vertex: $( 0,0 )$ focus: $\left( 0 , \frac { 7 } { 9 } \right)$ 
B)  vertex: $( 0,0 )$ focus: $\left( \frac { 7 } { 9 } , 0 \right)$ 
C)  vertex: $( 0,0 )$ focus: $\left( \frac { 7 } { 36 } , 0 \right)$ 
D)  vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( \frac { 7 } { 9 } , \frac { 7 } { 9 } \right)$ 
E)  vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( 0 , \frac { 7 } { 36 } \right)$ 
A)  vertex: $( 0,0 )$ focus: $\left( 0 , \frac { 7 } { 9 } \right)$ 
B)  vertex: $( 0,0 )$ focus: $\left( \frac { 7 } { 9 } , 0 \right)$ 
C)  vertex: $( 0,0 )$ focus: $\left( \frac { 7 } { 36 } , 0 \right)$ 
D)  vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( \frac { 7 } { 9 } , \frac { 7 } { 9 } \right)$ 
E)  vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( 0 , \frac { 7 } { 36 } \right)$

Question 17

Find the distance between the point and the line. Round your answer to four decimal places.

Accepted Answer

A)  $d \approx 0.9612$ 
B)  $d \approx 1.9612$ 
C)  $d \approx 4.9612$ 
D)  $d \approx 3.9612$ 
E)  $d \approx 2.9612$ 
A)  $d \approx 0.9612$ 
B)  $d \approx 1.9612$ 
C)  $d \approx 4.9612$ 
D)  $d \approx 3.9612$ 
E)  $d \approx 2.9612$

Question 18

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $\left( 7 , \frac { 11 \pi } { 9 } \right)$

Accepted Answer

A)  Rectangular coordinates: $( - 5.36 , - 4.50 )$ 
B)  Rectangular coordinates: $( - 5.36,0.11 )$ 
C)  Rectangular coordinates: $( - 4.50 , - 5.36 )$ 
D)  Rectangular coordinates: $( - 5.36,4.50 )$ 
E)  Rectangular coordinates: $( 4.50 , - 5.36 )$ 
A)  Rectangular coordinates: $( - 5.36 , - 4.50 )$ 
B)  Rectangular coordinates: $( - 5.36,0.11 )$ 
C)  Rectangular coordinates: $( - 4.50 , - 5.36 )$ 
D)  Rectangular coordinates: $( - 5.36,4.50 )$ 
E)  Rectangular coordinates: $( 4.50 , - 5.36 )$

Question 19

Convert the rectangular equation to polar form. Assume 
$a > 0$ 
$y = - 7$

Accepted Answer

A)  $r = - \csc \theta$ 
B)  $r = - 7 \sec \theta$ 
C)  $r = - 7 \csc \theta$ 
D)  $r = - 7 \cos \theta$ 
E)  $r = - 7 \sin \theta$ 
A)  $r = - \csc \theta$ 
B)  $r = - 7 \sec \theta$ 
C)  $r = - 7 \csc \theta$ 
D)  $r = - 7 \cos \theta$ 
E)  $r = - 7 \sin \theta$

Question 20

Select the curve represented by the parametric equations. $\text { Prolate cycloid: } x = \theta - \frac { 7 } { 6 } \sin \theta , y = 1 - \frac { 7 } { 6 } \cos \theta$

Accepted Answer

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

Find the slope of the line with inclination $\theta$ . Round your answer to four decimal places. $\theta = 2.26 \text { radians }$

Find the center and vertices of the ellipse. $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 4 } = 1$

Convert the rectangular equation to polar form. Assume $a > 0$ $x y = 10$

Find the standard form of the equation of the parabola with the given characteristics. $\text { Vertex: } ( 1,3 ) \text {; directrix: } y = - 2$

Select the polar equation with graph.

Find the center, vertices and foci of the hyperbola. $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 64 } = 1$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. $\text { Vertices: } ( \pm 5,0 ) \text {; asymptotes: } y = \pm 9 x$

Find the slope of the line with inclination $\theta$ . Round your answer to four decimal places. $\theta = 2.88 \text { radians }$

Consider a line with slope m and y-intercept $( 0,8 )$ Write the distance d between the point $( 7,1 )$ and the line as a function of m.

Identify the conic as a circle or an ellipse then find the radius. $\frac { x ^ { 2 } } { 36 / 49 } + \frac { ( y + 1 ) ^ { 2 } } { 36 / 49 } = 1$

Consider a line with slope m and y-intercept $( 0,6 )$ Select the graph of the distance between the origin and the line.

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=52\theta y=52\theta

Select the curve represented by the parametric equations. $\text { Prolate cycloid: } x = \theta - \frac { 5 } { 4 } \sin \theta , y = 1 - \frac { 5 } { 4 } \cos \theta$

Give the standard form of the equation of the parabola with the given characteristics.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = - 3$

Find the vertex and focus of the parabola. $y ^ { 2 } = \frac { 7 } { 9 } x$

Find the distance between the point and the line. Round your answer to four decimal places.

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $\left( 7 , \frac { 11 \pi } { 9 } \right)$

Convert the rectangular equation to polar form. Assume $a > 0$ $y = - 7$

Select the curve represented by the parametric equations. $\text { Prolate cycloid: } x = \theta - \frac { 7 } { 6 } \sin \theta , y = 1 - \frac { 7 } { 6 } \cos \theta$

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Exam 6: Topics in Analytic Geometry

Find the slope of the line with inclination θ\thetaθ . Round your answer to four decimal places. θ=2.26 radians \theta = 2.26 \text { radians }θ=2.26 radians

Find the center and vertices of the ellipse. x249+y24=1\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 4 } = 149x2​+4y2​=1

Convert the rectangular equation to polar form. Assume a>0a > 0a>0 xy=10x y = 10xy=10

Find the standard form of the equation of the parabola with the given characteristics. Vertex: (1,3); directrix: y=−2\text { Vertex: } ( 1,3 ) \text {; directrix: } y = - 2 Vertex: (1,3); directrix: y=−2

Select the polar equation with graph.

Find the center, vertices and foci of the hyperbola. x281−y264=1\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 64 } = 181x2​−64y2​=1

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (±5,0); asymptotes: y=±9x\text { Vertices: } ( \pm 5,0 ) \text {; asymptotes: } y = \pm 9 x Vertices: (±5,0); asymptotes: y=±9x

Find the slope of the line with inclination θ\thetaθ . Round your answer to four decimal places. θ=2.88 radians \theta = 2.88 \text { radians }θ=2.88 radians

Consider a line with slope m and y-intercept (0,8)( 0,8 )(0,8) Write the distance d between the point (7,1)( 7,1 )(7,1) and the line as a function of m.

Identify the conic as a circle or an ellipse then find the radius. x236/49+(y+1)236/49=1\frac { x ^ { 2 } } { 36 / 49 } + \frac { ( y + 1 ) ^ { 2 } } { 36 / 49 } = 136/49x2​+36/49(y+1)2​=1

Consider a line with slope m and y-intercept (0,6)( 0,6 )(0,6) Select the graph of the distance between the origin and the line.

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=52\theta y=52\theta

Select the curve represented by the parametric equations. Prolate cycloid: x=θ−54sin⁡θ,y=1−54cos⁡θ\text { Prolate cycloid: } x = \theta - \frac { 5 } { 4 } \sin \theta , y = 1 - \frac { 5 } { 4 } \cos \theta Prolate cycloid: x=θ−45​sinθ,y=1−45​cosθ

Give the standard form of the equation of the parabola with the given characteristics.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=−3r = - 3r=−3

Find the vertex and focus of the parabola. y2=79xy ^ { 2 } = \frac { 7 } { 9 } xy2=97​x

Find the distance between the point and the line. Round your answer to four decimal places.

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. (7,11π9)\left( 7 , \frac { 11 \pi } { 9 } \right)(7,911π​)

Convert the rectangular equation to polar form. Assume a>0a > 0a>0 y=−7y = - 7y=−7

Select the curve represented by the parametric equations. Prolate cycloid: x=θ−76sin⁡θ,y=1−76cos⁡θ\text { Prolate cycloid: } x = \theta - \frac { 7 } { 6 } \sin \theta , y = 1 - \frac { 7 } { 6 } \cos \theta Prolate cycloid: x=θ−67​sinθ,y=1−67​cosθ

Functions and Their Graphs

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Find the slope of the line with inclination $\theta$ . Round your answer to four decimal places. $\theta = 2.26 \text { radians }$

Find the center and vertices of the ellipse. $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 4 } = 1$

Convert the rectangular equation to polar form. Assume $a > 0$ $x y = 10$

Find the standard form of the equation of the parabola with the given characteristics. $\text { Vertex: } ( 1,3 ) \text {; directrix: } y = - 2$

Find the center, vertices and foci of the hyperbola. $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 64 } = 1$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. $\text { Vertices: } ( \pm 5,0 ) \text {; asymptotes: } y = \pm 9 x$

Find the slope of the line with inclination $\theta$ . Round your answer to four decimal places. $\theta = 2.88 \text { radians }$

Consider a line with slope m and y-intercept $( 0,8 )$ Write the distance d between the point $( 7,1 )$ and the line as a function of m.

Identify the conic as a circle or an ellipse then find the radius. $\frac { x ^ { 2 } } { 36 / 49 } + \frac { ( y + 1 ) ^ { 2 } } { 36 / 49 } = 1$

Consider a line with slope m and y-intercept $( 0,6 )$ Select the graph of the distance between the origin and the line.

Select the curve represented by the parametric equations. $\text { Prolate cycloid: } x = \theta - \frac { 5 } { 4 } \sin \theta , y = 1 - \frac { 5 } { 4 } \cos \theta$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = - 3$

Find the vertex and focus of the parabola. $y ^ { 2 } = \frac { 7 } { 9 } x$

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $\left( 7 , \frac { 11 \pi } { 9 } \right)$

Convert the rectangular equation to polar form. Assume $a > 0$ $y = - 7$

Select the curve represented by the parametric equations. $\text { Prolate cycloid: } x = \theta - \frac { 7 } { 6 } \sin \theta , y = 1 - \frac { 7 } { 6 } \cos \theta$