Question 1

Select the curve represented by the parametric equations. 
Cycloid: $x = 5 ( \Theta - \sin \theta ) , y = 5 ( 1 - \cos \theta )$

Accepted Answer

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

Question 2

The $x ^ { \prime } y ^ { \prime }$ -coordinate system has been rotated $\theta$ degrees from the $x y$ -coordinate system.The coordinates of a point in the $x y$ -coordinate system are given.Find the coordinates of the point in the rotated coordinate system.  $\theta = 45 ^ { \circ }$ , $( 9,2 )$

Accepted Answer

A)  $\left( \frac { 11 \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right)$ 
B)  $\left( - \frac { 11 \sqrt { 2 } } { 2 } , - \frac { 7 \sqrt { 2 } } { 2 } \right)$ 
C)  $\left( \frac { 11 } { 2 } , - \frac { 7 \sqrt { 2 } } { 2 } \right)$ 
D)  $\left( \frac { 11 \sqrt { 2 } } { 2 } , \frac { 7 \sqrt { 2 } } { 2 } \right)$ 
E)  $\left( \frac { 11 \sqrt { 2 } } { 2 } , - \frac { 7 \sqrt { 2 } } { 2 } \right)$ 
A)  $\left( \frac { 11 \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right)$ 
B)  $\left( - \frac { 11 \sqrt { 2 } } { 2 } , - \frac { 7 \sqrt { 2 } } { 2 } \right)$ 
C)  $\left( \frac { 11 } { 2 } , - \frac { 7 \sqrt { 2 } } { 2 } \right)$ 
D)  $\left( \frac { 11 \sqrt { 2 } } { 2 } , \frac { 7 \sqrt { 2 } } { 2 } \right)$ 
E)  $\left( \frac { 11 \sqrt { 2 } } { 2 } , - \frac { 7 \sqrt { 2 } } { 2 } \right)$

Question 3

Select the graph of degenerate conic.  $x ^ { 2 } - 14 x y + y ^ { 2 } = 0$

Accepted Answer

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

Question 4

By using a graphing utility select the correct graph of the polar equation.Identify the graph.  $\frac { 4 } { 1 - 2 \cos \theta }$

Accepted Answer

A)    $e = 2 > 1 \Rightarrow$ Hyperbola 
B)   $e = 2 > 1 \Rightarrow$ Hyperbola 
C)    $e = 2 > 1 \Rightarrow$ Hyperbola 
D)   $e = 2 > 1 \Rightarrow$ Hyperbola 
E)    $e = 2 > 1 \Rightarrow$ Hyperbola 
A)    $e = 2 > 1 \Rightarrow$ Hyperbola 
B)   $e = 2 > 1 \Rightarrow$ Hyperbola 
C)    $e = 2 > 1 \Rightarrow$ Hyperbola 
D)   $e = 2 > 1 \Rightarrow$ Hyperbola 
E)    $e = 2 > 1 \Rightarrow$ Hyperbola

Question 5

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.  $\left( 2 , \frac { 2 \pi } { 15 } \right)$

Accepted Answer

A) Rectangular coordinates: (1.83,-0.81) 
B) Rectangular coordinates: (1.83,1.83) 
C) Rectangular coordinates: (-0.81,0.81) 
D) Rectangular coordinates: (1.83,0.15) 
E) Rectangular coordinates: (1.83,0.81) 
A) Rectangular coordinates: (1.83,-0.81) 
B) Rectangular coordinates: (1.83,1.83) 
C) Rectangular coordinates: (-0.81,0.81) 
D) Rectangular coordinates: (1.83,0.15) 
E) Rectangular coordinates: (1.83,0.81)

Question 6

Select the curve represented by the parametric equations.  $x = t + 2$ $y = t ^ { 2 }$

Accepted Answer

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

Question 7

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0.  $( - 2,0 )$

Accepted Answer

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

Question 8

Use the discriminant to classify the graph.  $16 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 44 = 0$

Accepted Answer

A) The graph is a hyperbola. 
B) The graph is a line. 
C) The graph is a ellipse or Circle. 
D) The graph is a parabola. 
E) The graph is a cone. 
A) The graph is a hyperbola. 
B) The graph is a line. 
C) The graph is a ellipse or Circle. 
D) The graph is a parabola. 
E) The graph is a cone.

Question 9

Find the center and foci of the ellipse. $\frac { ( x - 2 ) ^ { 2 } } { 45 } + \frac { ( y - 8 ) ^ { 2 } } { 81 } = 1$

Accepted Answer

A) center: $( - 2 , - 8 )$ ; foci: $( - 2 , - 14 ) , ( - 2 , - 2 )$ 
B) center: $( 2,8 )$ ; foci: $( 2,2 ) , ( 2,14 )$ 
C) center: $( 2,8 )$ ; foci: $( 14,8 ) , ( 8,8 )$ 
D) center: $( - 2 , - 8 )$ ; foci: $( - 8,8 ) , ( - 14,8 )$ 
E) center: $( 2,8 )$ ; foci: $( - 8 , - 8 ) , ( - 14 , - 8 )$ 
A) center: $( - 2 , - 8 )$ ; foci: $( - 2 , - 14 ) , ( - 2 , - 2 )$ 
B) center: $( 2,8 )$ ; foci: $( 2,2 ) , ( 2,14 )$ 
C) center: $( 2,8 )$ ; foci: $( 14,8 ) , ( 8,8 )$ 
D) center: $( - 2 , - 8 )$ ; foci: $( - 8,8 ) , ( - 14,8 )$ 
E) center: $( 2,8 )$ ; foci: $( - 8 , - 8 ) , ( - 14 , - 8 )$

Question 10

Select the graph of the equation.  $r = 4 \sec \left( \theta + \frac { \pi } { 3 } \right)$

Accepted Answer

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

Question 11

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0.  $( - 13 , - 13 )$

Accepted Answer

A) Polar coordinates: $\left( \sqrt { 338 } , \frac { 5 \pi } { 4 } \right)$ 
B) Polar coordinates: $\left( - \sqrt { 338 } , \frac { 5 \pi } { 4 } \right)$ 
C) Polar coordinates: $\left( - \sqrt { 13 } , \frac { \pi } { 4 } \right)$ 
D) Polar coordinates: $\left( \sqrt { 13 } , \frac { \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 338 } , - \frac { \pi } { 4 } \right)$ 
A) Polar coordinates: $\left( \sqrt { 338 } , \frac { 5 \pi } { 4 } \right)$ 
B) Polar coordinates: $\left( - \sqrt { 338 } , \frac { 5 \pi } { 4 } \right)$ 
C) Polar coordinates: $\left( - \sqrt { 13 } , \frac { \pi } { 4 } \right)$ 
D) Polar coordinates: $\left( \sqrt { 13 } , \frac { \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 338 } , - \frac { \pi } { 4 } \right)$

Question 12

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $r = ( 1 + \sin \theta )$

Accepted Answer

A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 2 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 2 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 2 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$   
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 2 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 2 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 2 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 2 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 2 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$   
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 2 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$    
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 2 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$

Question 13

Find the vertex, focus, and directrix of the parabola.  $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = 4 ( y - 1 )$

Accepted Answer

A) Vertex: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Directrix: $y = 0$ 
B) Vertex: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Directrix: $y = 1$ 
C) Vertex: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Directrix: $y = 0$ 
D) Vertex: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Directrix: $y = 1$ 
E) Vertex: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Directrix: $y = 1$ 
A) Vertex: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Directrix: $y = 0$ 
B) Vertex: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Directrix: $y = 1$ 
C) Vertex: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Directrix: $y = 0$ 
D) Vertex: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Directrix: $y = 1$ 
E) Vertex: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Directrix: $y = 1$

Question 14

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola.  $3 x ^ { 2 } - 3 y ^ { 2 } - 3 x + 6 y + 17 = 0$

Accepted Answer

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

Question 15

Find the angle $$\theta$$ (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.
$$\begin{array} { l } 
6 x + y = 6 \
x - y = 5
\end{array}$$

Accepted Answer

A)  $\theta \approx 0.9505 \text { radians } \approx 54.5 ^ { \circ }$ 
B)  $\theta \approx 0.9505 \text { radians } \approx 55.5 ^ { \circ }$ 
C)  $\theta \approx 0.9505 \text { radians } \approx 53.5 ^ { \circ }$ 
D)  $\theta \approx 0.9505 \text { radians } \approx 56.5 ^ { \circ }$ 
E)  $\theta \approx 0.9505 \text { radians } \approx 52.5 ^ { \circ }$ 
A)  $\theta \approx 0.9505 \text { radians } \approx 54.5 ^ { \circ }$ 
B)  $\theta \approx 0.9505 \text { radians } \approx 55.5 ^ { \circ }$ 
C)  $\theta \approx 0.9505 \text { radians } \approx 53.5 ^ { \circ }$ 
D)  $\theta \approx 0.9505 \text { radians } \approx 56.5 ^ { \circ }$ 
E)  $\theta \approx 0.9505 \text { radians } \approx 52.5 ^ { \circ }$

Question 16

Select the correct graph of the polar equation.Find an interval for $\theta$ for which the graph is traced only once.  $r = 4 \sin \left( \frac { 5 \theta } { 2 } \right)$

Accepted Answer

A)    $0 \leq \theta < 4 \pi$ 
B)    $0 \leq \theta < 4 \pi$ 
C)    $0 \leq \theta < 4 \pi$ 
D)    $0 \leq \theta < 4 \pi$ 
E)   $0 \leq \theta < 4 \pi$ 
A)    $0 \leq \theta < 4 \pi$ 
B)    $0 \leq \theta < 4 \pi$ 
C)    $0 \leq \theta < 4 \pi$ 
D)    $0 \leq \theta < 4 \pi$ 
E)   $0 \leq \theta < 4 \pi$

Question 17

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -1)

Accepted Answer

A) y2 = -4x 
B) x2 = -4y 
C) x2 = y 
D) y2 = -x 
E) x2 = -y 
A) y2 = -4x 
B) x2 = -4y 
C) x2 = y 
D) y2 = -x 
E) x2 = -y

Question 18

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: $( 0 , \pm 6 )$ foci: $( 0 , \pm 8 )$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 64 } = 1$ 
B)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 28 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 28 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 28 } = 1$ 
E)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 28 } = 64$ 
A)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 64 } = 1$ 
B)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 28 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 28 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 28 } = 1$ 
E)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 28 } = 64$

Question 19

Find the inclination $\theta$ (in radians and degrees) of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.  $( - 2,20 ) , ( 10,0 )$

Accepted Answer

A)  $\theta \approx 2.1112 \text { radians } \approx 122.0 ^ { \circ }$ 
B)  $\theta \approx 2.1112 \text { radians } \approx 120.0 ^ { \circ }$ 
C)  $\theta \approx 2.1112 \text { radians } \approx 123.0 ^ { \circ }$ 
D)  $\theta \approx 2.1112 \text { radians } \approx 119.0 ^ { \circ }$ 
E)  $\theta \approx 2.1112 \text { radians } \approx 121.0 ^ { \circ }$ 
A)  $\theta \approx 2.1112 \text { radians } \approx 122.0 ^ { \circ }$ 
B)  $\theta \approx 2.1112 \text { radians } \approx 120.0 ^ { \circ }$ 
C)  $\theta \approx 2.1112 \text { radians } \approx 123.0 ^ { \circ }$ 
D)  $\theta \approx 2.1112 \text { radians } \approx 119.0 ^ { \circ }$ 
E)  $\theta \approx 2.1112 \text { radians } \approx 121.0 ^ { \circ }$

Question 20

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​
A = (0,0), B = (3,6), C = (6,0)
​

Accepted Answer

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

Select the curve represented by the parametric equations. Cycloid: $x = 5 ( \Theta - \sin \theta ) , y = 5 ( 1 - \cos \theta )$

The $x ^ { \prime } y ^ { \prime }$ -coordinate system has been rotated $\theta$ degrees from the $x y$ -coordinate system.The coordinates of a point in the $x y$ -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. $\theta = 45 ^ { \circ }$ , $( 9,2 )$

Select the graph of degenerate conic. $x ^ { 2 } - 14 x y + y ^ { 2 } = 0$

By using a graphing utility select the correct graph of the polar equation.Identify the graph. $\frac { 4 } { 1 - 2 \cos \theta }$

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $\left( 2 , \frac { 2 \pi } { 15 } \right)$

Select the curve represented by the parametric equations. $x = t + 2$ $y = t ^ { 2 }$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( - 2,0 )$

Use the discriminant to classify the graph. $16 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 44 = 0$

Find the center and foci of the ellipse. $\frac { ( x - 2 ) ^ { 2 } } { 45 } + \frac { ( y - 8 ) ^ { 2 } } { 81 } = 1$

Select the graph of the equation. $r = 4 \sec \left( \theta + \frac { \pi } { 3 } \right)$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( - 13 , - 13 )$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = ( 1 + \sin \theta )$

Find the vertex, focus, and directrix of the parabola. $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = 4 ( y - 1 )$

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola. $3 x ^ { 2 } - 3 y ^ { 2 } - 3 x + 6 y + 17 = 0$

Select the correct graph of the polar equation.Find an interval for $\theta$ for which the graph is traced only once. $r = 4 \sin \left( \frac { 5 \theta } { 2 } \right)$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -1)

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: $( 0 , \pm 6 )$ foci: $( 0 , \pm 8 )$

Find the inclination $\theta$ (in radians and degrees) of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $( - 2,20 ) , ( 10,0 )$

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. A = (0,0), B = (3,6), C = (6,0)

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 10: Topics In Analytic Geometry

Select the curve represented by the parametric equations. Cycloid: x=5(Θ−sin⁡θ),y=5(1−cos⁡θ)x = 5 ( \Theta - \sin \theta ) , y = 5 ( 1 - \cos \theta )x=5(Θ−sinθ),y=5(1−cosθ)

Select the graph of degenerate conic. x2−14xy+y2=0x ^ { 2 } - 14 x y + y ^ { 2 } = 0x2−14xy+y2=0

By using a graphing utility select the correct graph of the polar equation.Identify the graph. 41−2cos⁡θ\frac { 4 } { 1 - 2 \cos \theta }1−2cosθ4​

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. (2,2π15)\left( 2 , \frac { 2 \pi } { 15 } \right)(2,152π​)

Select the curve represented by the parametric equations. x=t+2x = t + 2x=t+2 y=t2y = t ^ { 2 }y=t2

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. (−2,0)( - 2,0 )(−2,0)

Use the discriminant to classify the graph. 16x2−5xy+10y2−44=016 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 44 = 016x2−5xy+10y2−44=0

Find the center and foci of the ellipse. (x−2)245+(y−8)281=1\frac { ( x - 2 ) ^ { 2 } } { 45 } + \frac { ( y - 8 ) ^ { 2 } } { 81 } = 145(x−2)2​+81(y−8)2​=1

Select the graph of the equation. r=4sec⁡(θ+π3)r = 4 \sec \left( \theta + \frac { \pi } { 3 } \right)r=4sec(θ+3π​)

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. (−13,−13)( - 13 , - 13 )(−13,−13)

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=(1+sin⁡θ)r = ( 1 + \sin \theta )r=(1+sinθ)

Find the vertex, focus, and directrix of the parabola. (x+72)2=4(y−1)\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = 4 ( y - 1 )(x+27​)2=4(y−1)

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola. 3x2−3y2−3x+6y+17=03 x ^ { 2 } - 3 y ^ { 2 } - 3 x + 6 y + 17 = 03x2−3y2−3x+6y+17=0

Find the angle θ\thetaθ (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. 6x+y=6 x-y=5

Select the correct graph of the polar equation.Find an interval for θ\thetaθ for which the graph is traced only once. r=4sin⁡(5θ2)r = 4 \sin \left( \frac { 5 \theta } { 2 } \right)r=4sin(25θ​)

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -1)

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (0,±6)( 0 , \pm 6 )(0,±6) foci: (0,±8)( 0 , \pm 8 )(0,±8)

Find the inclination θ\thetaθ (in radians and degrees) of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. (−2,20),(10,0)( - 2,20 ) , ( 10,0 )(−2,20),(10,0)

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​ A = (0,0), B = (3,6), C = (6,0) ​

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Select the curve represented by the parametric equations. Cycloid: $x = 5 ( \Theta - \sin \theta ) , y = 5 ( 1 - \cos \theta )$

Select the graph of degenerate conic. $x ^ { 2 } - 14 x y + y ^ { 2 } = 0$

By using a graphing utility select the correct graph of the polar equation.Identify the graph. $\frac { 4 } { 1 - 2 \cos \theta }$

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $\left( 2 , \frac { 2 \pi } { 15 } \right)$

Select the curve represented by the parametric equations. $x = t + 2$ $y = t ^ { 2 }$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( - 2,0 )$

Use the discriminant to classify the graph. $16 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 44 = 0$

Find the center and foci of the ellipse. $\frac { ( x - 2 ) ^ { 2 } } { 45 } + \frac { ( y - 8 ) ^ { 2 } } { 81 } = 1$

Select the graph of the equation. $r = 4 \sec \left( \theta + \frac { \pi } { 3 } \right)$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( - 13 , - 13 )$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = ( 1 + \sin \theta )$

Find the vertex, focus, and directrix of the parabola. $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = 4 ( y - 1 )$

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola. $3 x ^ { 2 } - 3 y ^ { 2 } - 3 x + 6 y + 17 = 0$

Select the correct graph of the polar equation.Find an interval for $\theta$ for which the graph is traced only once. $r = 4 \sin \left( \frac { 5 \theta } { 2 } \right)$

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: $( 0 , \pm 6 )$ foci: $( 0 , \pm 8 )$

Find the inclination $\theta$ (in radians and degrees) of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $( - 2,20 ) , ( 10,0 )$

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. A = (0,0), B = (3,6), C = (6,0)