Question 1

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

Accepted Answer

A)  $y = x ^ { 2 } + 10 x + 25$ 
B)  $y = x ^ { 2 } - 10 x + 25$ 
C)  $y = t + 5$ 
D)  $y = x ^ { 2 }$ 
E)  $y = t - 5$ 
A)  $y = x ^ { 2 } + 10 x + 25$ 
B)  $y = x ^ { 2 } - 10 x + 25$ 
C)  $y = t + 5$ 
D)  $y = x ^ { 2 }$ 
E)  $y = t - 5$

Question 2

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. $\text { Directrix: } y = 6$

Accepted Answer

A)  $y ^ { 2 } = 24 x$ 
B)  $y ^ { 2 } = x$ 
C)  $y ^ { 2 } = - 24 x$ 
D)  $x ^ { 2 } = - 24 y$ 
E)  $x ^ { 2 } = 24 y$ 
A)  $y ^ { 2 } = 24 x$ 
B)  $y ^ { 2 } = x$ 
C)  $y ^ { 2 } = - 24 x$ 
D)  $x ^ { 2 } = - 24 y$ 
E)  $x ^ { 2 } = 24 y$

Question 3

By using a graphing utility select the correct graph of the polar equation. Identify the graph. $\frac { 14 } { 14 + 18 \sin \theta }$

Accepted Answer

A) 
 
$ e=\frac{9}{7}>1 \Rightarrow $ Hyperabola 
B) 
 
$ e=\frac{9}{7}>1 \Rightarrow $ Hyperabola 
C) 
 
$ e=\frac{9}{7}>1 \Rightarrow $ Hyperabola 
D) 
 
$ e=\frac{9}{7}>1 \Rightarrow $ Hyperabola 
E) 
 
$ e=\frac{9}{7}>1 \Rightarrow $ Hyperabola 
A) 
 
$ e=\frac{9}{7}>1 \Rightarrow $ Hyperabola 
B) 
 
$ e=\frac{9}{7}>1 \Rightarrow $ Hyperabola 
C) 
 
$ e=\frac{9}{7}>1 \Rightarrow $ Hyperabola 
D) 
 
$ e=\frac{9}{7}>1 \Rightarrow $ Hyperabola 
E) 
 
$ e=\frac{9}{7}>1 \Rightarrow $ Hyperabola

Question 4

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 2 \sin \theta$

Accepted Answer

A)  Symmetric with respect to $\theta = \frac { \pi } { 2 } \quad$ Circle with radius 1
  
B)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$ Circle with radius 1
  
C)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$ Circle with radius 1
  
D)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$ Circle with radius 1
  
E)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$ Circle with radius 1 
  
A)  Symmetric with respect to $\theta = \frac { \pi } { 2 } \quad$ Circle with radius 1
  
B)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$ Circle with radius 1
  
C)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$ Circle with radius 1
  
D)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$ Circle with radius 1
  
E)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$ Circle with radius 1

Question 5

Find the Eccentricity of the conic. $$\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 16 } = 1$$

Accepted Answer

A) 
Eccentricity: $e = \frac { \sqrt { 84 } } { 4 }$ 
B) 
Eccentricity: $e = \frac { \sqrt { 100 } } { 4 }$ 
C) 
Eccentricity: $e = \frac { \sqrt { 84 } } { 100 }$ 
D) 
Eccentricity: $e = \frac { 4 \sqrt { 84 } } { 84 }$ 
E) 
Eccentricity: $e = \frac { \sqrt { 84 } } { 10 }$ 
A) 
Eccentricity: $e = \frac { \sqrt { 84 } } { 4 }$ 
B) 
Eccentricity: $e = \frac { \sqrt { 100 } } { 4 }$ 
C) 
Eccentricity: $e = \frac { \sqrt { 84 } } { 100 }$ 
D) 
Eccentricity: $e = \frac { 4 \sqrt { 84 } } { 84 }$ 
E) 
Eccentricity: $e = \frac { \sqrt { 84 } } { 10 }$

Question 6

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $$23 x ^ { 2 } - 10 x - 200 y - 117 = 0$$

Accepted Answer

A)  Hyperbola 
B)  Circle 
C)  Parabola 
D)  Ellipse 
E)  None of the above 
A)  Hyperbola 
B)  Circle 
C)  Parabola 
D)  Ellipse 
E)  None of the above

Question 7

Select the parametric equations matching with the following graph.

Accepted Answer

A) 
Involute of circle: $x = \frac { 1 } { 3 } ( \cos \theta + \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta - \theta \cos \theta )$ 
B) 
Involute of circle: $x = \frac { 1 } { 3 } ( \cos \theta - \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta + \cos \theta )$ 
C) 
Involute of circle: $x = \frac { 1 } { 3 } ( \cos \theta - \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta - \theta \cos \theta )$ 
D)  Involute of circle: $x = \frac { 1 } { 3 } ( \cos \theta + \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta + \theta \cos \theta )$ 
E) 
Involute of circle: $x = \frac { 1 } { 3 } ( \cos \theta + \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta - \cos \theta )$ 
A) 
Involute of circle: $x = \frac { 1 } { 3 } ( \cos \theta + \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta - \theta \cos \theta )$ 
B) 
Involute of circle: $x = \frac { 1 } { 3 } ( \cos \theta - \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta + \cos \theta )$ 
C) 
Involute of circle: $x = \frac { 1 } { 3 } ( \cos \theta - \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta - \theta \cos \theta )$ 
D)  Involute of circle: $x = \frac { 1 } { 3 } ( \cos \theta + \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta + \theta \cos \theta )$ 
E) 
Involute of circle: $x = \frac { 1 } { 3 } ( \cos \theta + \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta - \cos \theta )$

Question 8

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r ^ { 2 } = 9 \sin \theta$

Accepted Answer

A)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$
  
B)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$
  
C) 
$$\begin{array} { l } 
r = 3 \sqrt { \sin \theta } \
r = - 3 \sqrt { \sin \theta } \
0 \leq \theta \leq \pi
\end{array}$$
  
D)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$
  
E)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$
  
A)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$
  
B)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$
  
C) 
$$\begin{array} { l } 
r = 3 \sqrt { \sin \theta } \
r = - 3 \sqrt { \sin \theta } \
0 \leq \theta \leq \pi
\end{array}$$
  
D)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$
  
E)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$

Question 9

Find the standard form of the equation of the ellipse with the given characteristics. foci: $( 4,3 ) , ( 4,13 )$endpoints of the major axis: $( 4,0 ) , ( 4,16 )$

Accepted Answer

A) $\frac { x + 8 ^ { 2 } } { 64 } + \frac { y + 4 ^ { 2 } } { 39 } = 1$ 
B)  $\frac { x - 4 ^ { 2 } } { 64 } + \frac { y - 8 ^ { 2 } } { 39 } = 1$ 
C)  $\frac { x + 4 ^ { 2 } } { 39 } + \frac { y + 8 ^ { 2 } } { 64 } = 1$ 
D)  $\frac { x - 4 ^ { 2 } } { 39 } + \frac { y - 8 ^ { 2 } } { 64 } = 1$ 
E)  $\frac { x - 8 ^ { 2 } } { 64 } + \frac { y - 4 ^ { 2 } } { 39 } = 1$ 
A) $\frac { x + 8 ^ { 2 } } { 64 } + \frac { y + 4 ^ { 2 } } { 39 } = 1$ 
B)  $\frac { x - 4 ^ { 2 } } { 64 } + \frac { y - 8 ^ { 2 } } { 39 } = 1$ 
C)  $\frac { x + 4 ^ { 2 } } { 39 } + \frac { y + 8 ^ { 2 } } { 64 } = 1$ 
D)  $\frac { x - 4 ^ { 2 } } { 39 } + \frac { y - 8 ^ { 2 } } { 64 } = 1$ 
E)  $\frac { x - 8 ^ { 2 } } { 64 } + \frac { y - 4 ^ { 2 } } { 39 } = 1$

Question 10

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 2 + 6 \sin \theta$

Accepted Answer

A)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$
$| r | = 8$ when $\theta = \frac { \pi } { 2 }$
$r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$
  
B)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$
$| r | = 8$ when $\theta = \frac { \pi } { 2 }$
$r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$
  
C) 
Symmetric with respect to $\theta = \frac { \pi } { 2 }$
$| r | = 8$ when $\theta = \frac { \pi } { 2 }$
$r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$
  
D) 
Symmetric with respect to $\theta = \frac { \pi } { 2 }$
$| r | = 8$ when $\theta = \frac { \pi } { 2 }$
$r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$
  
E)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$
$| r | = 8$ when $\theta = \frac { \pi } { 2 }$
$r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$
  
A)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$
$| r | = 8$ when $\theta = \frac { \pi } { 2 }$
$r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$
  
B)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$
$| r | = 8$ when $\theta = \frac { \pi } { 2 }$
$r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$
  
C) 
Symmetric with respect to $\theta = \frac { \pi } { 2 }$
$| r | = 8$ when $\theta = \frac { \pi } { 2 }$
$r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$
  
D) 
Symmetric with respect to $\theta = \frac { \pi } { 2 }$
$| r | = 8$ when $\theta = \frac { \pi } { 2 }$
$r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$
  
E)  Symmetric with respect to $\theta = \frac { \pi } { 2 }$
$| r | = 8$ when $\theta = \frac { \pi } { 2 }$
$r = 0$ when $\theta = \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$

Question 11

A point in polar coordinates is given. Convert the point to rectangular coordinates. Round your answers to one decimal places. $( - 2.9,1.3 )$

Accepted Answer

A)  Rectangular coordinates: $( 2.8,0.8 )$ 
B)  Rectangular coordinates: $( - 0.8 , - 2.8 )$ 
C)  Rectangular coordinates: $( 2.9,1.3 )$ 
D)  Rectangular coordinates: $( - 2.8 , - 0.8 )$ 
E)  Rectangular coordinates: $( 0.8,2.8 )$ 
A)  Rectangular coordinates: $( 2.8,0.8 )$ 
B)  Rectangular coordinates: $( - 0.8 , - 2.8 )$ 
C)  Rectangular coordinates: $( 2.9,1.3 )$ 
D)  Rectangular coordinates: $( - 2.8 , - 0.8 )$ 
E)  Rectangular coordinates: $( 0.8,2.8 )$

Question 12

Convert the polar equation to rectangular form $r = 6 \csc \theta$

Accepted Answer

A)  $y = 6$ 
B)  $y = 6 r$ 
C)  $x = 6$ 
D)  $6 y = r$ 
E)  $x = 6 r$ 
A)  $y = 6$ 
B)  $y = 6 r$ 
C)  $x = 6$ 
D)  $6 y = r$ 
E)  $x = 6 r$

Question 13

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

Accepted Answer

A)  $d \approx 4.2403$ 
B)  $d \approx 2.2403$ 
C)  $d \approx 1.2403$ 
D)  $d \approx 3.2403$ 
E)  $d \approx 0.2403$ 
A)  $d \approx 4.2403$ 
B)  $d \approx 2.2403$ 
C)  $d \approx 1.2403$ 
D)  $d \approx 3.2403$ 
E)  $d \approx 0.2403$

Question 14

A point in rectangular coordinates is given. Convert the point to polar coordinates. $( 4,4 )$

Accepted Answer

A)  Polar coordinates: $\left( \sqrt { 4 } , \frac { \pi } { 4 } \right)$ 
B)  Polar coordinates: $\left( - \sqrt { 4 } , \frac { \pi } { 4 } \right)$ 
C)  Polar coordinates: $\left( 4 \sqrt { 2 } , \frac { \pi } { 4 } \right)$ 
D)  Polar coordinates: $\left( - 4 \sqrt { 2 } , \frac { \pi } { 4 } \right)$ 
E)  Polar coordinates: $\left( 4 \sqrt { 2 } , - \frac { \pi } { 4 } \right)$ 
A)  Polar coordinates: $\left( \sqrt { 4 } , \frac { \pi } { 4 } \right)$ 
B)  Polar coordinates: $\left( - \sqrt { 4 } , \frac { \pi } { 4 } \right)$ 
C)  Polar coordinates: $\left( 4 \sqrt { 2 } , \frac { \pi } { 4 } \right)$ 
D)  Polar coordinates: $\left( - 4 \sqrt { 2 } , \frac { \pi } { 4 } \right)$ 
E)  Polar coordinates: $\left( 4 \sqrt { 2 } , - \frac { \pi } { 4 } \right)$

Question 15

Identify the conic and select its correct graph. $r = \frac { 8 } { 2 - \cos \theta }$

Accepted Answer

A)  $\quad e = 2 > 1 \Rightarrow$ Hyperbola
  
B)  $e = \frac { 1 } { 2 } 1 \Rightarrow \text { Hyperbola }$
  
D)  $\quad e = \frac { 1 } { 2 }  1 \Rightarrow$ Hyperbola
  
A)  $\quad e = 2 > 1 \Rightarrow$ Hyperbola
  
B)  $e = \frac { 1 } { 2 } 1 \Rightarrow \text { Hyperbola }$
  
D)  $\quad e = \frac { 1 } { 2 }  1 \Rightarrow$ Hyperbola

Question 16

Find the inclination $\theta$ (in degrees) of the line with a slope of $m$ . Round your answer to one decimal places. $m = - \frac { 3 } { 2 }$

Accepted Answer

A)  $\theta \approx 124.7 ^ { \circ }$ 
B)  $\theta \approx 122.7 ^ { \circ }$ 
C)  $\theta \approx 125.7 ^ { \circ }$ 
D)  $\theta \approx 121.7 ^ { \circ }$ 
E)  $\theta \approx 123.7 ^ { \circ }$ 
A)  $\theta \approx 124.7 ^ { \circ }$ 
B)  $\theta \approx 122.7 ^ { \circ }$ 
C)  $\theta \approx 125.7 ^ { \circ }$ 
D)  $\theta \approx 121.7 ^ { \circ }$ 
E)  $\theta \approx 123.7 ^ { \circ }$

Question 17

Identify the conic and select its correct graph. 
$r = \frac { 6 } { 2 - 12 \cos \theta }$

Accepted Answer

A)  $\quad e = 6 > 1 \Rightarrow$ Hyperbola
  
B)  $e = 6 > 1 \Rightarrow$ Hyperbola
  
C)   $e=6>1 \Rightarrow \text { Hyperbola }$
  
D)  $\quad e = 2 > 1 \Rightarrow$ Hyperbola
  
E)  $e = 6 > 1 \Rightarrow$ Hyperbola
  
A)  $\quad e = 6 > 1 \Rightarrow$ Hyperbola
  
B)  $e = 6 > 1 \Rightarrow$ Hyperbola
  
C)   $e=6>1 \Rightarrow \text { Hyperbola }$
  
D)  $\quad e = 2 > 1 \Rightarrow$ Hyperbola
  
E)  $e = 6 > 1 \Rightarrow$ Hyperbola

Question 18

Identify the conic and select its correct graph. $r = \frac { 3 } { 1 - \cos \theta }$

Accepted Answer

A)  $\quad e = 1 \Rightarrow$ Parabola
  
B)  $e = 2 \Rightarrow$ Hyperabola
  
C)  $\quad e = 1 \Rightarrow$ Parabola
  
D)  $\quad e = 1 \Rightarrow$ Parabola
  
E)  $e = 1 \Rightarrow$ Parabola
  
A)  $\quad e = 1 \Rightarrow$ Parabola
  
B)  $e = 2 \Rightarrow$ Hyperabola
  
C)  $\quad e = 1 \Rightarrow$ Parabola
  
D)  $\quad e = 1 \Rightarrow$ Parabola
  
E)  $e = 1 \Rightarrow$ Parabola

Question 19

Select the correct graph of the following equations of the hyperbola and find the cen- ter of the hyperbola. $\frac { ( y + 3 ) ^ { 2 } } { 1 / 16 } + \frac { ( x - 2 ) ^ { 2 } } { 1 / 9 } = 1$

Accepted Answer

A) 
$\text { Center: }(2,-3)$
  
B) $\text { Center: }(0,0)$
  
C)  $\text { Center: }(2,-3)$
  
D)  Center: $( 0,0 )$
  
E)  $\text { Center: }(2,-3)$
  
A) 
$\text { Center: }(2,-3)$
  
B) $\text { Center: }(0,0)$
  
C)  $\text { Center: }(2,-3)$
  
D)  Center: $( 0,0 )$
  
E)  $\text { Center: }(2,-3)$

Question 20

Select the graph of $r = 3 \cos \theta$ over the interval. Describe the part of the graph ob- tained in this case. $- \frac { \pi } { 2 } \leq \theta \leq \frac { \pi } { 2 }$

Accepted Answer

A) 
 
Entire circle 
B) 
 
Entire circle 
C) 
 
$\text { Entire circle }$ 
D) 
 
Entire circle 
E) 
 
Entire circle 
A) 
 
Entire circle 
B) 
 
Entire circle 
C) 
 
$\text { Entire circle }$ 
D) 
 
Entire circle 
E) 
 
Entire circle

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=t+5 y=

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. $\text { Directrix: } y = 6$

By using a graphing utility select the correct graph of the polar equation. Identify the graph. $\frac { 14 } { 14 + 18 \sin \theta }$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 2 \sin \theta$

Find the Eccentricity of the conic. $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 16 } = 1$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $23 x ^ { 2 } - 10 x - 200 y - 117 = 0$

Select the parametric equations matching with the following graph.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r ^ { 2 } = 9 \sin \theta$

Find the standard form of the equation of the ellipse with the given characteristics. foci: $( 4,3 ) , ( 4,13 )$ endpoints of the major axis: $( 4,0 ) , ( 4,16 )$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 2 + 6 \sin \theta$

A point in polar coordinates is given. Convert the point to rectangular coordinates. Round your answers to one decimal places. $( - 2.9,1.3 )$

Convert the polar equation to rectangular form $r = 6 \csc \theta$

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

A point in rectangular coordinates is given. Convert the point to polar coordinates. $( 4,4 )$

Identify the conic and select its correct graph. $r = \frac { 8 } { 2 - \cos \theta }$

Find the inclination $\theta$ (in degrees) of the line with a slope of $m$ . Round your answer to one decimal places. $m = - \frac { 3 } { 2 }$

Identify the conic and select its correct graph. $r = \frac { 6 } { 2 - 12 \cos \theta }$

Identify the conic and select its correct graph. $r = \frac { 3 } { 1 - \cos \theta }$

Select the correct graph of the following equations of the hyperbola and find the cen- ter of the hyperbola. $\frac { ( y + 3 ) ^ { 2 } } { 1 / 16 } + \frac { ( x - 2 ) ^ { 2 } } { 1 / 9 } = 1$

Select the graph of $r = 3 \cos \theta$ over the interval. Describe the part of the graph ob- tained in this case. $- \frac { \pi } { 2 } \leq \theta \leq \frac { \pi } { 2 }$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Filters

Exam 6: Topics in Analytic Geometry

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=t+5 y=

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Directrix: y=6\text { Directrix: } y = 6 Directrix: y=6

By using a graphing utility select the correct graph of the polar equation. Identify the graph. 1414+18sin⁡θ\frac { 14 } { 14 + 18 \sin \theta }14+18sinθ14​

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=2sin⁡θr = 2 \sin \thetar=2sinθ

Find the Eccentricity of the conic. x2100+y216=1\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 16 } = 1100x2​+16y2​=1

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 23x2−10x−200y−117=023 x ^ { 2 } - 10 x - 200 y - 117 = 023x2−10x−200y−117=0

Select the parametric equations matching with the following graph.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r2=9sin⁡θr ^ { 2 } = 9 \sin \thetar2=9sinθ

Find the standard form of the equation of the ellipse with the given characteristics. foci: (4,3),(4,13)( 4,3 ) , ( 4,13 )(4,3),(4,13) endpoints of the major axis: (4,0),(4,16)( 4,0 ) , ( 4,16 )(4,0),(4,16)

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=2+6sin⁡θr = 2 + 6 \sin \thetar=2+6sinθ

A point in polar coordinates is given. Convert the point to rectangular coordinates. Round your answers to one decimal places. (−2.9,1.3)( - 2.9,1.3 )(−2.9,1.3)

Convert the polar equation to rectangular form r=6csc⁡θr = 6 \csc \thetar=6cscθ

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

A point in rectangular coordinates is given. Convert the point to polar coordinates. (4,4)( 4,4 )(4,4)

Identify the conic and select its correct graph. r=82−cos⁡θr = \frac { 8 } { 2 - \cos \theta }r=2−cosθ8​

Find the inclination θ\thetaθ (in degrees) of the line with a slope of mmm . Round your answer to one decimal places. m=−32m = - \frac { 3 } { 2 }m=−23​

Identify the conic and select its correct graph. r=62−12cos⁡θr = \frac { 6 } { 2 - 12 \cos \theta }r=2−12cosθ6​

Identify the conic and select its correct graph. r=31−cos⁡θr = \frac { 3 } { 1 - \cos \theta }r=1−cosθ3​

Select the correct graph of the following equations of the hyperbola and find the cen- ter of the hyperbola. (y+3)21/16+(x−2)21/9=1\frac { ( y + 3 ) ^ { 2 } } { 1 / 16 } + \frac { ( x - 2 ) ^ { 2 } } { 1 / 9 } = 11/16(y+3)2​+1/9(x−2)2​=1

Select the graph of r=3cos⁡θr = 3 \cos \thetar=3cosθ over the interval. Describe the part of the graph ob- tained in this case. −π2≤θ≤π2- \frac { \pi } { 2 } \leq \theta \leq \frac { \pi } { 2 }−2π​≤θ≤2π​

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Filters

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. $\text { Directrix: } y = 6$

By using a graphing utility select the correct graph of the polar equation. Identify the graph. $\frac { 14 } { 14 + 18 \sin \theta }$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 2 \sin \theta$

Find the Eccentricity of the conic. $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 16 } = 1$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $23 x ^ { 2 } - 10 x - 200 y - 117 = 0$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r ^ { 2 } = 9 \sin \theta$

Find the standard form of the equation of the ellipse with the given characteristics. foci: $( 4,3 ) , ( 4,13 )$ endpoints of the major axis: $( 4,0 ) , ( 4,16 )$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 2 + 6 \sin \theta$

A point in polar coordinates is given. Convert the point to rectangular coordinates. Round your answers to one decimal places. $( - 2.9,1.3 )$

Convert the polar equation to rectangular form $r = 6 \csc \theta$

A point in rectangular coordinates is given. Convert the point to polar coordinates. $( 4,4 )$

Identify the conic and select its correct graph. $r = \frac { 8 } { 2 - \cos \theta }$

Find the inclination $\theta$ (in degrees) of the line with a slope of $m$ . Round your answer to one decimal places. $m = - \frac { 3 } { 2 }$

Identify the conic and select its correct graph. $r = \frac { 6 } { 2 - 12 \cos \theta }$

Identify the conic and select its correct graph. $r = \frac { 3 } { 1 - \cos \theta }$

Select the correct graph of the following equations of the hyperbola and find the cen- ter of the hyperbola. $\frac { ( y + 3 ) ^ { 2 } } { 1 / 16 } + \frac { ( x - 2 ) ^ { 2 } } { 1 / 9 } = 1$

Select the graph of $r = 3 \cos \theta$ over the interval. Describe the part of the graph ob- tained in this case. $- \frac { \pi } { 2 } \leq \theta \leq \frac { \pi } { 2 }$