Question 1

Graph the hyperbola.  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 25 } = 1$

Accepted Answer

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

Question 2

Give the coordinates of the circle's center and its radius.
  $x ^ { 2 } + y ^ { 2 } - 1 = 0$  
Enter your answer using the coordinate notation: (a, b) and r = ....separated with a comma.

Accepted Answer

The answer of Give the coordinates of the circle's center...

Question 3

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.  $( 0,200 ) , ( 20,0 )$

Accepted Answer

A)  $\Theta \approx 1.6705 \text { radians } \approx 96.7 ^ { \circ }$ 
B)  $\theta \approx 1.6705 \text { radians } \approx 94.7 ^ { \circ }$ 
C)  $\theta \approx 1.6705 \text { radians } \approx 97.7 ^ { \circ }$ 
D)  $\theta \approx 1.6705 \text { radians } \approx 95.7 ^ { \circ }$ 
E)  $\theta \approx 1.6705 \text { radians } \approx 93.7 ^ { \circ }$ 
A)  $\Theta \approx 1.6705 \text { radians } \approx 96.7 ^ { \circ }$ 
B)  $\theta \approx 1.6705 \text { radians } \approx 94.7 ^ { \circ }$ 
C)  $\theta \approx 1.6705 \text { radians } \approx 97.7 ^ { \circ }$ 
D)  $\theta \approx 1.6705 \text { radians } \approx 95.7 ^ { \circ }$ 
E)  $\theta \approx 1.6705 \text { radians } \approx 93.7 ^ { \circ }$

Question 4

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $( 0 , - 4 )$

Accepted Answer

A)  $x ^ { 2 } = 16 y$ 
B)  $y ^ { 2 } = x$ 
C)  $y ^ { 2 } = 16 x$ 
D)  $x ^ { 2 } = - 16 y$ 
E)  $y ^ { 2 } = - 16 x$ 
A)  $x ^ { 2 } = 16 y$ 
B)  $y ^ { 2 } = x$ 
C)  $y ^ { 2 } = 16 x$ 
D)  $x ^ { 2 } = - 16 y$ 
E)  $y ^ { 2 } = - 16 x$

Question 5

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places.  $( - 6,3.56 )$

Accepted Answer

A) Rectangular coordinates: (3.6,6.0) 
B) Rectangular coordinates: (5.5,2.4) 
C) Rectangular coordinates: (-5.5,-2.4) 
D) Rectangular coordinates: (-2.4,-5.5) 
E) Rectangular coordinates: (2.4,5.5) 
A) Rectangular coordinates: (3.6,6.0) 
B) Rectangular coordinates: (5.5,2.4) 
C) Rectangular coordinates: (-5.5,-2.4) 
D) Rectangular coordinates: (-2.4,-5.5) 
E) Rectangular coordinates: (2.4,5.5)

Question 6

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane.  $A = \left( - \frac { 1 } { 6 } , \frac { 1 } { 7 } \right) , B = ( 6,7 ) , C = \left( \frac { 6 } { 7 } , 0 \right)$

Accepted Answer

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

Question 7

Find the center, vertices and foci of the hyperbola.  $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 1 } = 1$

Accepted Answer

A) Center: (0, 0)Vertices: $( 0 , \pm 2 )$ Foci: $( 0 , \pm \sqrt { 5 } )$ 
B) Center: (0, 0)Vertices: $( \pm 2,0 )$ Foci: $( 0 , \pm \sqrt { 5 } )$ 
C) Center: $( 4,1 )$ Vertices: $( \pm 2,0 )$ Foci: $( \pm \sqrt { 5 } , 0 )$ 
D) Center: $( 4,1 )$ Vertices: $( 0 , \pm 2 )$ Foci: $( 0 , \pm \sqrt { 5 } )$ 
E) Center: (0, 0)Vertices: $( \pm 2,0 )$ Foci: $( \pm \sqrt { 5 } , 0 )$ 
A) Center: (0, 0)Vertices: $( 0 , \pm 2 )$ Foci: $( 0 , \pm \sqrt { 5 } )$ 
B) Center: (0, 0)Vertices: $( \pm 2,0 )$ Foci: $( 0 , \pm \sqrt { 5 } )$ 
C) Center: $( 4,1 )$ Vertices: $( \pm 2,0 )$ Foci: $( \pm \sqrt { 5 } , 0 )$ 
D) Center: $( 4,1 )$ Vertices: $( 0 , \pm 2 )$ Foci: $( 0 , \pm \sqrt { 5 } )$ 
E) Center: (0, 0)Vertices: $( \pm 2,0 )$ Foci: $( \pm \sqrt { 5 } , 0 )$

Question 8

A moving conveyor is built so that it rises 7 meter for each 9 meters of horizontal travel.Select a diagram that gives a visual representation of the problem. ​

Accepted Answer

A) ​   a = 7m, b = 9m 
B) ​   a = 7m, b = 9m 
C) ​   a = 7m, b = 9m 
D) ​   a = 7m, b = 9m 
E) ​   a = 7m, b = 9m 
A) ​   a = 7m, b = 9m 
B) ​   a = 7m, b = 9m 
C) ​   a = 7m, b = 9m 
D) ​   a = 7m, b = 9m 
E) ​   a = 7m, b = 9m

Question 9

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 10

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $r = 4 - 5 \cos \theta$

Accepted Answer

A) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$$    
B) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$$    
C) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$$    
D) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$$    
E) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$$    
A) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$$    
B) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$$    
C) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$$    
D) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$$    
E) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$$

Question 11

Find the center and vertices of the ellipse.  $x ^ { 2 } + 4 y ^ { 2 } - 18 x + 64 y + 333 = 0$

Accepted Answer

A) center: (-8, 9), vertices: (-10, 9), (-6, 9) 
B) center: (9, -8), vertices: (7, -8), (11, -8) 
C) center: (-9, 8), vertices: (-10, 8), (-8, 8) 
D) center: (-9, 8), vertices: (-11, 8), (-7, 8) 
E) center: (9, -8), vertices: (8, -8), (10, -8) 
A) center: (-8, 9), vertices: (-10, 9), (-6, 9) 
B) center: (9, -8), vertices: (7, -8), (11, -8) 
C) center: (-9, 8), vertices: (-10, 8), (-8, 8) 
D) center: (-9, 8), vertices: (-11, 8), (-7, 8) 
E) center: (9, -8), vertices: (8, -8), (10, -8)

Question 12

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

Question 13

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places.  $x ^ { 2 } + 2 x y + y ^ { 2 } = 10$

Accepted Answer

A)  $\theta = 45 ^ { \circ }$ 
B)  $\theta = 60 ^ { \circ }$ 
C)  $\theta = 90 ^ { \circ }$ 
D)  $\theta = 145 ^ { \circ }$ 
E)  $\theta = 30 ^ { \circ }$ 
A)  $\theta = 45 ^ { \circ }$ 
B)  $\theta = 60 ^ { \circ }$ 
C)  $\theta = 90 ^ { \circ }$ 
D)  $\theta = 145 ^ { \circ }$ 
E)  $\theta = 30 ^ { \circ }$

Question 14

Find the inclination $\theta$ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $8 x - 2 y + 14 = 0$

Accepted Answer

A)  $\theta \approx 1.4289 \text { radians } \approx 82.9 ^ { \circ }$ 
B)  $\Theta \approx 1.4289 \text { radians } \approx 80.9 ^ { \circ }$ 
C)  $\theta \approx 1.4289 \text { radians } \approx 83.9 ^ { \circ }$ 
D)  $\theta \approx 1.4289 \text { radians } \approx 79.9 ^ { \circ }$ 
E)  $\theta \approx 1.4289 \text { radians } \approx 81.9 ^ { \circ }$ 
A)  $\theta \approx 1.4289 \text { radians } \approx 82.9 ^ { \circ }$ 
B)  $\Theta \approx 1.4289 \text { radians } \approx 80.9 ^ { \circ }$ 
C)  $\theta \approx 1.4289 \text { radians } \approx 83.9 ^ { \circ }$ 
D)  $\theta \approx 1.4289 \text { radians } \approx 79.9 ^ { \circ }$ 
E)  $\theta \approx 1.4289 \text { radians } \approx 81.9 ^ { \circ }$

Question 15

Identify the conic and select its correct graph.  $r = \frac { 2 } { 2 + 3 \sin \theta }$

Accepted Answer

A)  $e = \frac { 3 } { 2 } > 1 \Rightarrow$ Hyperbola   
B)  $e = \frac { 3 } { 2 } > 1 \Rightarrow$ Hyperbola   
C)  $e = \frac { 3 } { 2 } > 1 \Rightarrow$ Hyperbola   
D)  $e = \frac { 3 } { 2 } > 1 \Rightarrow$ Hyperbola   
E)  $e = \frac { 3 } { 2 } > 1 \Rightarrow$ Hyperbola   
A)  $e = \frac { 3 } { 2 } > 1 \Rightarrow$ Hyperbola   
B)  $e = \frac { 3 } { 2 } > 1 \Rightarrow$ Hyperbola   
C)  $e = \frac { 3 } { 2 } > 1 \Rightarrow$ Hyperbola   
D)  $e = \frac { 3 } { 2 } > 1 \Rightarrow$ Hyperbola   
E)  $e = \frac { 3 } { 2 } > 1 \Rightarrow$ Hyperbola

Question 16

Find the slope of the line with inclination $\Theta$ .Round your answer to four decimal places.  $\Theta = 1.41 \text { radians }$

Accepted Answer

A)  $m \approx 7.1654$ 
B)  $m \approx 5.1654$ 
C)  $m \approx 8.1654$ 
D)  $m \approx 6.1654$ 
E)  $m \approx 4.1654$ 
A)  $m \approx 7.1654$ 
B)  $m \approx 5.1654$ 
C)  $m \approx 8.1654$ 
D)  $m \approx 6.1654$ 
E)  $m \approx 4.1654$

Question 17

Use the Quadratic Formula to solve for $y$ .  $x ^ { 2 } + x y + 4 y ^ { 2 } + x + y - 4 = 0$

Accepted Answer

A)  $y = \frac { ( x + 1 ) \pm \sqrt { ( x - 1 ) ^ { 2 } - 8 \left( x ^ { 2 } - x + 4 \right) } } { 4 }$ 
B)  $y = \frac { - ( x + 1 ) \pm \sqrt { ( x + 1 ) ^ { 2 } - 8 \left( x ^ { 2 } + x + 4 \right) } } { 4 }$ 
C)  $y = \frac { - ( x + 1 ) \pm \sqrt { ( x + 1 ) ^ { 2 } - 8 \left( x ^ { 2 } + x - 4 \right) } } { 4 }$ 
D)  $y = \frac { ( x + 1 ) \pm \sqrt { ( x + 1 ) ^ { 2 } - 8 \left( x ^ { 2 } + x - 4 \right) } } { 4 }$ 
E)  $y = \frac { - ( x + 1 ) \pm \sqrt { ( x + 1 ) ^ { 2 } + 8 \left( x ^ { 2 } + x - 4 \right) } } { 4 }$ 
A)  $y = \frac { ( x + 1 ) \pm \sqrt { ( x - 1 ) ^ { 2 } - 8 \left( x ^ { 2 } - x + 4 \right) } } { 4 }$ 
B)  $y = \frac { - ( x + 1 ) \pm \sqrt { ( x + 1 ) ^ { 2 } - 8 \left( x ^ { 2 } + x + 4 \right) } } { 4 }$ 
C)  $y = \frac { - ( x + 1 ) \pm \sqrt { ( x + 1 ) ^ { 2 } - 8 \left( x ^ { 2 } + x - 4 \right) } } { 4 }$ 
D)  $y = \frac { ( x + 1 ) \pm \sqrt { ( x + 1 ) ^ { 2 } - 8 \left( x ^ { 2 } + x - 4 \right) } } { 4 }$ 
E)  $y = \frac { - ( x + 1 ) \pm \sqrt { ( x + 1 ) ^ { 2 } + 8 \left( x ^ { 2 } + x - 4 \right) } } { 4 }$

Question 18

The Falls Incline Railway in Niagara Falls, Ontario, Canada is an inclined railway that was designed to carry people from the City of Niagara Falls to Queen Victoria Park.The railway is approximately 130 feet long with a 46% uphill grade (see figure).Find the inclination $\theta$ of the railway.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.    $$a = 130$$

Accepted Answer

A)  $\Theta \approx 0.4311 \text { radian, or } 25.7 ^ { \circ }$ 
B)  $\Theta \approx 0.4311 \text { radian, or } 23.7 ^ { \circ }$ 
C)  $\Theta \approx 0.4311 \text { radian, or } 26.7 ^ { \circ }$ 
D)  $\Theta \approx 0.4311 \text { radian, or } 24.7 ^ { \circ }$ 
E)  $\Theta \approx 0.4311 \text { radian, or } 22.7 ^ { \circ }$ 
A)  $\Theta \approx 0.4311 \text { radian, or } 25.7 ^ { \circ }$ 
B)  $\Theta \approx 0.4311 \text { radian, or } 23.7 ^ { \circ }$ 
C)  $\Theta \approx 0.4311 \text { radian, or } 26.7 ^ { \circ }$ 
D)  $\Theta \approx 0.4311 \text { radian, or } 24.7 ^ { \circ }$ 
E)  $\Theta \approx 0.4311 \text { radian, or } 22.7 ^ { \circ }$

Question 19

Find the distance between the point and the line.Round your answer to four decimal places.  Point Line
$$( 14,12 ) \quad 11 x - y = 0$$

Accepted Answer

A)  $d \approx 2.1626$ 
B)  $d \approx 3.1626$ 
C)  $d \approx 1.1626$ 
D)  $d \approx 0.1626$ 
E)  $d \approx 4.1626$ 
A)  $d \approx 2.1626$ 
B)  $d \approx 3.1626$ 
C)  $d \approx 1.1626$ 
D)  $d \approx 0.1626$ 
E)  $d \approx 4.1626$

Question 20

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph.  $r = 2 \sec \theta$

Accepted Answer

A) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first. $x - 5 = 0$    
B) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first. $x - 2 = 0$    
C) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first. $x + 2 = 0$    
D) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first. $x - 3 = 0$    
E) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first. $x - 3 = 0$    
A) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first. $x - 5 = 0$    
B) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first. $x - 2 = 0$    
C) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first. $x + 2 = 0$    
D) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first. $x - 3 = 0$    
E) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first. $x - 3 = 0$

Graph the hyperbola. $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 25 } = 1$

Give the coordinates of the circle's center and its radius. $x ^ { 2 } + y ^ { 2 } - 1 = 0$ Enter your answer using the coordinate notation: (a, b) and r = ....separated with a comma.

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. $( 0,200 ) , ( 20,0 )$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $( 0 , - 4 )$

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places. $( - 6,3.56 )$

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. $A = \left( - \frac { 1 } { 6 } , \frac { 1 } { 7 } \right) , B = ( 6,7 ) , C = \left( \frac { 6 } { 7 } , 0 \right)$

Find the center, vertices and foci of the hyperbola. $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 1 } = 1$

A moving conveyor is built so that it rises 7 meter for each 9 meters of horizontal travel.Select a diagram that gives a visual representation of the problem.

Select the polar equation with graph.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 4 - 5 \cos \theta$

Find the center and vertices of the ellipse. $x ^ { 2 } + 4 y ^ { 2 } - 18 x + 64 y + 333 = 0$

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

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $x ^ { 2 } + 2 x y + y ^ { 2 } = 10$

Find the inclination $\theta$ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $8 x - 2 y + 14 = 0$

Identify the conic and select its correct graph. $r = \frac { 2 } { 2 + 3 \sin \theta }$

Find the slope of the line with inclination $\Theta$ .Round your answer to four decimal places. $\Theta = 1.41 \text { radians }$

Use the Quadratic Formula to solve for $y$ . $x ^ { 2 } + x y + 4 y ^ { 2 } + x + y - 4 = 0$

Find the distance between the point and the line.Round your answer to four decimal places. Point Line $( 14,12 ) \quad 11 x - y = 0$

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. $r = 2 \sec \theta$

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

Graph the hyperbola. y225−x225=1\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 25 } = 125y2​−25x2​=1

Give the coordinates of the circle's center and its radius. x2+y2−1=0x ^ { 2 } + y ^ { 2 } - 1 = 0x2+y2−1=0 Enter your answer using the coordinate notation: (a, b) and r = ....separated with a comma.

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. (0,200),(20,0)( 0,200 ) , ( 20,0 )(0,200),(20,0)

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: (0,−4)( 0 , - 4 )(0,−4)

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places. (−6,3.56)( - 6,3.56 )(−6,3.56)

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. A=(−16,17),B=(6,7),C=(67,0)A = \left( - \frac { 1 } { 6 } , \frac { 1 } { 7 } \right) , B = ( 6,7 ) , C = \left( \frac { 6 } { 7 } , 0 \right)A=(−61​,71​),B=(6,7),C=(76​,0)

Find the center, vertices and foci of the hyperbola. y24−x21=1\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 1 } = 14y2​−1x2​=1

A moving conveyor is built so that it rises 7 meter for each 9 meters of horizontal travel.Select a diagram that gives a visual representation of the problem. ​

Select the polar equation with graph.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=4−5cos⁡θr = 4 - 5 \cos \thetar=4−5cosθ

Find the center and vertices of the ellipse. x2+4y2−18x+64y+333=0x ^ { 2 } + 4 y ^ { 2 } - 18 x + 64 y + 333 = 0x2+4y2−18x+64y+333=0

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

Determine the angle θ\thetaθ through which the axes are rotated.Round your answer to two decimal places. x2+2xy+y2=10x ^ { 2 } + 2 x y + y ^ { 2 } = 10x2+2xy+y2=10

Find the inclination θ\thetaθ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. 8x−2y+14=08 x - 2 y + 14 = 08x−2y+14=0

Identify the conic and select its correct graph. r=22+3sin⁡θr = \frac { 2 } { 2 + 3 \sin \theta }r=2+3sinθ2​

Find the slope of the line with inclination Θ\ThetaΘ .Round your answer to four decimal places. Θ=1.41 radians \Theta = 1.41 \text { radians }Θ=1.41 radians

Use the Quadratic Formula to solve for yyy . x2+xy+4y2+x+y−4=0x ^ { 2 } + x y + 4 y ^ { 2 } + x + y - 4 = 0x2+xy+4y2+x+y−4=0

Find the distance between the point and the line.Round your answer to four decimal places. Point Line (14,12)11x−y=0( 14,12 ) \quad 11 x - y = 0(14,12)11x−y=0

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. r=2sec⁡θr = 2 \sec \thetar=2secθ

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

Graph the hyperbola. $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 25 } = 1$

Give the coordinates of the circle's center and its radius. $x ^ { 2 } + y ^ { 2 } - 1 = 0$ Enter your answer using the coordinate notation: (a, b) and r = ....separated with a comma.

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. $( 0,200 ) , ( 20,0 )$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $( 0 , - 4 )$

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places. $( - 6,3.56 )$

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. $A = \left( - \frac { 1 } { 6 } , \frac { 1 } { 7 } \right) , B = ( 6,7 ) , C = \left( \frac { 6 } { 7 } , 0 \right)$

Find the center, vertices and foci of the hyperbola. $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 1 } = 1$

A moving conveyor is built so that it rises 7 meter for each 9 meters of horizontal travel.Select a diagram that gives a visual representation of the problem.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 4 - 5 \cos \theta$

Find the center and vertices of the ellipse. $x ^ { 2 } + 4 y ^ { 2 } - 18 x + 64 y + 333 = 0$

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

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $x ^ { 2 } + 2 x y + y ^ { 2 } = 10$

Find the inclination $\theta$ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $8 x - 2 y + 14 = 0$

Identify the conic and select its correct graph. $r = \frac { 2 } { 2 + 3 \sin \theta }$

Find the slope of the line with inclination $\Theta$ .Round your answer to four decimal places. $\Theta = 1.41 \text { radians }$

Use the Quadratic Formula to solve for $y$ . $x ^ { 2 } + x y + 4 y ^ { 2 } + x + y - 4 = 0$

Find the distance between the point and the line.Round your answer to four decimal places. Point Line $( 14,12 ) \quad 11 x - y = 0$

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. $r = 2 \sec \theta$