Question 1

Find the standard form of the equation of the parabola with the given characteristics. 
Vertex: $( 6,5 )$ ; focus: $( 8,5 )$

Accepted Answer

A)  $( y - 6 ) ^ { 2 } = 8 ( x - 5 )$ 
B)  $( y - 5 ) ^ { 2 } = 8 ( x - 6 )$ 
C)  $( x - 6 ) ^ { 2 } = - 8 ( y - 5 )$ 
D)  $( y - 6 ) ^ { 2 } = - 8 ( x - 5 )$ 
E)  $( x - 5 ) ^ { 2 } = 8 ( y - 6 )$ 
A)  $( y - 6 ) ^ { 2 } = 8 ( x - 5 )$ 
B)  $( y - 5 ) ^ { 2 } = 8 ( x - 6 )$ 
C)  $( x - 6 ) ^ { 2 } = - 8 ( y - 5 )$ 
D)  $( y - 6 ) ^ { 2 } = - 8 ( x - 5 )$ 
E)  $( x - 5 ) ^ { 2 } = 8 ( y - 6 )$ B

Question 2

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places.  $17 x ^ { 2 } + 72 x y - 3 y ^ { 2 } = 77$

Accepted Answer

A)  $\theta = 79.87 ^ { \circ }$ 
B)  $\theta = 77.87 ^ { \circ }$ 
C)  $\theta = 80.87 ^ { \circ }$ 
D)  $\theta = 81.87 ^ { \circ }$ 
E)  $\theta = 78.87 ^ { \circ }$ 
A)  $\theta = 79.87 ^ { \circ }$ 
B)  $\theta = 77.87 ^ { \circ }$ 
C)  $\theta = 80.87 ^ { \circ }$ 
D)  $\theta = 81.87 ^ { \circ }$ 
E)  $\theta = 78.87 ^ { \circ }$ B

Question 3

Convert the rectangular equation to polar form.Assume r > 1.  $x = 17 a$

Accepted Answer

A)  $\gamma = \operatorname { acsc } \theta$ 
B)  $r = 17 \mathrm { a } \cos \theta$ 
C)  $r = 17 \sin \theta$ 
D)  $r = 17 \operatorname { acsc } \theta$ 
E)  $r = 17 \text { asec } \theta$ 
A)  $\gamma = \operatorname { acsc } \theta$ 
B)  $r = 17 \mathrm { a } \cos \theta$ 
C)  $r = 17 \sin \theta$ 
D)  $r = 17 \operatorname { acsc } \theta$ 
E)  $r = 17 \text { asec } \theta$ E

Question 4

Select the parametric equations matching with the following graph.

Accepted Answer

A) Lissajous curve: $x = 2 \cos \Theta , y = 2 \sin \Theta$ 
B) Lissajous curve: $x = 2 \cos 2 \Theta , y = 2 \sin 2 \Theta$ 
C) Lissajous curve: $x = 2 \cos \Theta , y = 2 \sin 2 \Theta$ 
D) Lissajous curve: $x = 2 \cos \Theta , y = \sin 2 \Theta$ , 
E) Lissajous curve: $x = 2 \cos 2 \Theta , y = \sin 2 \Theta$ 
A) Lissajous curve: $x = 2 \cos \Theta , y = 2 \sin \Theta$ 
B) Lissajous curve: $x = 2 \cos 2 \Theta , y = 2 \sin 2 \Theta$ 
C) Lissajous curve: $x = 2 \cos \Theta , y = 2 \sin 2 \Theta$ 
D) Lissajous curve: $x = 2 \cos \Theta , y = \sin 2 \Theta$ , 
E) Lissajous curve: $x = 2 \cos 2 \Theta , y = \sin 2 \Theta$

Question 5

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. 
Directrix: $y = 3$

Accepted Answer

A)  $y ^ { 2 } = - 12 x$ 
B)  $y ^ { 2 } = x$ 
C)  $y ^ { 2 } = 12 x$ 
D)  $x ^ { 2 } = 12 y$ 
E)  $x ^ { 2 } = - 12 y$ 
A)  $y ^ { 2 } = - 12 x$ 
B)  $y ^ { 2 } = x$ 
C)  $y ^ { 2 } = 12 x$ 
D)  $x ^ { 2 } = 12 y$ 
E)  $x ^ { 2 } = - 12 y$

Question 6

Find the center and vertices of the ellipse.  $x ^ { 2 } + 9 y ^ { 2 } + 16 x + 18 y + 64 = 0$

Accepted Answer

A) center: $( - 1 , - 8 )$ vertices: $( - 4 , - 8 ) , ( 9 , - 8 )$ 
B) center: $( 8,1 )$ vertices: $( 7,1 ) , ( 9,1 )$ 
C) center: $( - 8 , - 1 )$ vertices: $( - 9 , - 1 ) , ( - 7 , - 1 )$ 
D) center: $( - 8 , - 1 )$ vertices: $( - 11 , - 1 ) , ( - 5 , - 1 )$ 
E) center: $( 8,1 )$ vertices: $( 5,1 ) , ( - 11,1 )$ 
A) center: $( - 1 , - 8 )$ vertices: $( - 4 , - 8 ) , ( 9 , - 8 )$ 
B) center: $( 8,1 )$ vertices: $( 7,1 ) , ( 9,1 )$ 
C) center: $( - 8 , - 1 )$ vertices: $( - 9 , - 1 ) , ( - 7 , - 1 )$ 
D) center: $( - 8 , - 1 )$ vertices: $( - 11 , - 1 ) , ( - 5 , - 1 )$ 
E) center: $( 8,1 )$ vertices: $( 5,1 ) , ( - 11,1 )$

Question 7

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. 
Parabola: $x ^ { 2 } + 20 y = 0$ Tangent Line: $x + y - 5 = 0$

Accepted Answer

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

Question 8

Find the vertex and focus of the parabola from the given equation and select its graph.  $x ^ { 2 } + 16 y = 0$

Accepted Answer

A) Vertex: (0,0)Focus: (4,0)   
B) Vertex: (0,0)Focus: (-4,0)   
C) Vertex: (0,-4)Focus: (0,0)   
D) Vertex: (0,0)Focus: (0,4)   
E) Vertex: (0,0)Focus: (0,-4)   
A) Vertex: (0,0)Focus: (4,0)   
B) Vertex: (0,0)Focus: (-4,0)   
C) Vertex: (0,-4)Focus: (0,0)   
D) Vertex: (0,0)Focus: (0,4)   
E) Vertex: (0,0)Focus: (0,-4)

Question 9

Select the graph of degenerate conic.  $x ^ { 2 } + 2 x y + y ^ { 2 } - 9 = 0$

Accepted Answer

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

Question 10

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. $r = 7 \csc \theta$

Accepted Answer

A) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first.$$y + 7 = 0$$    
B) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first. $y - 6 = 0$    
C) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first.$y - 9 = 0$    
D) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first.$y - 7 = 0$   
E) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first. $y - 8 = 0$    
A) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first.$$y + 7 = 0$$    
B) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first. $y - 6 = 0$    
C) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first.$y - 9 = 0$    
D) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first.$y - 7 = 0$   
E) The graph of the polar equation is not evident by simple inspection. Convert to rectangular form first. $y - 8 = 0$

Question 11

Convert the rectangular equation to polar form.Assume r > 1. $y = - 3$

Accepted Answer

A)  $r = - 3 \sec \theta$ 
B)  $r = - 3 \csc \theta$ 
C)  $r = - \csc \theta$ 
D)  $r = - 3 \cos \theta$ 
E)  $r = - 3 \sin \theta$ 
A)  $r = - 3 \sec \theta$ 
B)  $r = - 3 \csc \theta$ 
C)  $r = - \csc \theta$ 
D)  $r = - 3 \cos \theta$ 
E)  $r = - 3 \sin \theta$

Question 12

Select the correct graph of the polar equation.Describe your viewing window.  $r = \frac { 7 } { 4 }$

Accepted Answer

A)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$ 
B)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$ 
C)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$ 
D)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$ 
E)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$ 
A)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$ 
B)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$ 
C)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$ 
D)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$ 
E)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$

Question 13

Find the vertex, focus, and directrix of the parabola.  $( x + 3 ) + ( y - 1 ) ^ { 2 } = 0$

Accepted Answer

A) Vertex: $( - 3,1 )$ ; Focus: $\left( \frac { - 13 } { 4 } , 1 \right)$ ; Directrix: $x = \frac { - 11 } { 4 }$ 
B) Vertex: $( 1 , - 3 , )$ ; Focus: $\left( 1 , \frac { - 11 } { 4 } \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$ 
C) Vertex: $( 1 , - 3 , )$ ; Focus: $\left( \frac { - 11 } { 4 } , 1 \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$ 
D) Vertex: $( - 3,1 )$ ; Focus: $\left( 1 , \frac { - 13 } { 4 } \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$ 
E) Vertex: $( - 3,1 )$ ; Focus: $\left( 1 , \frac { - 11 } { 4 } \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$ 
A) Vertex: $( - 3,1 )$ ; Focus: $\left( \frac { - 13 } { 4 } , 1 \right)$ ; Directrix: $x = \frac { - 11 } { 4 }$ 
B) Vertex: $( 1 , - 3 , )$ ; Focus: $\left( 1 , \frac { - 11 } { 4 } \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$ 
C) Vertex: $( 1 , - 3 , )$ ; Focus: $\left( \frac { - 11 } { 4 } , 1 \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$ 
D) Vertex: $( - 3,1 )$ ; Focus: $\left( 1 , \frac { - 13 } { 4 } \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$ 
E) Vertex: $( - 3,1 )$ ; Focus: $\left( 1 , \frac { - 11 } { 4 } \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$

Question 14

Find the distance between the point and the line.Round your answer to four decimal places.  Point Line
$( 2,3 ) \quad x - y = 2$

Accepted Answer

A)  $d \approx 6.6569$ 
B)  $d \approx 7.6569$ 
C)  $d \approx 4.6569$ 
D)  $d \approx 8.6569$ 
E)  $d \approx 5.6569$ 
A)  $d \approx 6.6569$ 
B)  $d \approx 7.6569$ 
C)  $d \approx 4.6569$ 
D)  $d \approx 8.6569$ 
E)  $d \approx 5.6569$

Question 15

Find the center, vertices and foci of the hyperbola.  $5 x ^ { 2 } - 6 y ^ { 2 } = 30$

Accepted Answer

A) Center: (1, 1)Vertices: $( 0 , \pm \sqrt { 6 } )$ Foci: $( 0 , \pm \sqrt { 11 } )$ 
B) Center: $( 5,6 )$ Vertices: $( \pm \sqrt { 6 } , 0 )$ Foci: $( \pm \sqrt { 11 } , 0 )$ 
C) Center: (0, 0)Vertices: $( 0 , \pm \sqrt { 6 } )$ Foci: $( 0 , \pm \sqrt { 11 } )$ 
D) Center: (0, 0)Vertices: $( \pm \sqrt { 6 } , 0 )$ Foci: $( \pm \sqrt { 11 } , 0 )$ 
E) Center: $( 6,5 )$ Vertices: $( \pm \sqrt { 6 } , 0 )$ Foci: $( \pm \sqrt { 11 } , 0 )$ 
A) Center: (1, 1)Vertices: $( 0 , \pm \sqrt { 6 } )$ Foci: $( 0 , \pm \sqrt { 11 } )$ 
B) Center: $( 5,6 )$ Vertices: $( \pm \sqrt { 6 } , 0 )$ Foci: $( \pm \sqrt { 11 } , 0 )$ 
C) Center: (0, 0)Vertices: $( 0 , \pm \sqrt { 6 } )$ Foci: $( 0 , \pm \sqrt { 11 } )$ 
D) Center: (0, 0)Vertices: $( \pm \sqrt { 6 } , 0 )$ Foci: $( \pm \sqrt { 11 } , 0 )$ 
E) Center: $( 6,5 )$ Vertices: $( \pm \sqrt { 6 } , 0 )$ Foci: $( \pm \sqrt { 11 } , 0 )$

Question 16

Convert the rectangular equation to polar form.Assume r > 1.  $5 x + 7 y - 4 = 0$

Accepted Answer

A)  $y = \frac { - 4 } { 5 \cos \Theta - 7 \sin \theta }$ 
B)  $y = \frac { - 4 } { 5 \cos \Theta + 7 \sin \theta }$ 
C)  $y = \frac { 4 } { 5 \cos \Theta - 7 \sin \theta }$ 
D)  $y = \frac { 4 } { 5 \cos \Theta + 7 \sin \theta }$ 
E)  $y = \frac { 1 } { 5 \cos \Theta + 7 \sin \theta }$ 
A)  $y = \frac { - 4 } { 5 \cos \Theta - 7 \sin \theta }$ 
B)  $y = \frac { - 4 } { 5 \cos \Theta + 7 \sin \theta }$ 
C)  $y = \frac { 4 } { 5 \cos \Theta - 7 \sin \theta }$ 
D)  $y = \frac { 4 } { 5 \cos \Theta + 7 \sin \theta }$ 
E)  $y = \frac { 1 } { 5 \cos \Theta + 7 \sin \theta }$

Question 17

Find the vertex and focus of the parabola from the given equation and select its graph.  $y ^ { 2 } = 6 x$

Accepted Answer

A) Vertex: (0,0)Focus: (- $\frac { 3 } { 2 }$ ,0)   
B) Vertex: (0,0)Focus: (0,- $\frac { 3 } { 2 }$ )   
C) Vertex: (0,0)Focus: ( $\frac { 3 } { 2 }$ ,0)   
D) Vertex: (0,0)Focus: (0, $\frac { 3 } { 2 }$ )   
E) Vertex: (0,0)Focus: ( $\frac { 3 } { 2 }$ ,0)   
A) Vertex: (0,0)Focus: (- $\frac { 3 } { 2 }$ ,0)   
B) Vertex: (0,0)Focus: (0,- $\frac { 3 } { 2 }$ )   
C) Vertex: (0,0)Focus: ( $\frac { 3 } { 2 }$ ,0)   
D) Vertex: (0,0)Focus: (0, $\frac { 3 } { 2 }$ )   
E) Vertex: (0,0)Focus: ( $\frac { 3 } { 2 }$ ,0)

Question 18

Identify the conic.  $4 y ^ { 2 } - 8 x = 0$

Accepted Answer

A) Circle 
B) Ellipse 
C) Parabola 
D) Hyperbola 
E) Line 
A) Circle 
B) Ellipse 
C) Parabola 
D) Hyperbola 
E) Line

Question 19

After a rotation of axes is used to eliminate the $x y$ -term from an equation of the form $A x ^ { 2 } + B x y + C y ^ { 2 } + D x + B y + F = 0$ the coefficients of the $x ^ { 2 }$ -and $y ^ { 2 }$ -terms remain $A$ and $C$ , respectively.

Accepted Answer

A) True 
 B)False

Question 20

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 110 feet long with a 28% uphill grade (see figure).Find the change in elevation from the base to the top of the railway.Round your answers to one decimal place.     $$a = 110$$

Accepted Answer

A)  $z \approx 29.7 \mathrm { ft }$ 
B)  $z \approx 30.7 \mathrm { ft }$ 
C)  $z \approx 28.7 \mathrm { ft }$ 
D)  $z \approx 31.7 \mathrm { ft }$ 
E)  $z \approx 27.7 \mathrm { ft }$ 
A)  $z \approx 29.7 \mathrm { ft }$ 
B)  $z \approx 30.7 \mathrm { ft }$ 
C)  $z \approx 28.7 \mathrm { ft }$ 
D)  $z \approx 31.7 \mathrm { ft }$ 
E)  $z \approx 27.7 \mathrm { ft }$

Find the standard form of the equation of the parabola with the given characteristics. Vertex: $( 6,5 )$ ; focus: $( 8,5 )$

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $17 x ^ { 2 } + 72 x y - 3 y ^ { 2 } = 77$

Convert the rectangular equation to polar form.Assume r > 1. $x = 17 a$

Select the parametric equations matching with the following graph.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Directrix: $y = 3$

Find the center and vertices of the ellipse. $x ^ { 2 } + 9 y ^ { 2 } + 16 x + 18 y + 64 = 0$

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. Parabola: $x ^ { 2 } + 20 y = 0$ Tangent Line: $x + y - 5 = 0$

Find the vertex and focus of the parabola from the given equation and select its graph. $x ^ { 2 } + 16 y = 0$

Select the graph of degenerate conic. $x ^ { 2 } + 2 x y + y ^ { 2 } - 9 = 0$

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. $r = 7 \csc \theta$

Convert the rectangular equation to polar form.Assume r > 1. $y = - 3$

Select the correct graph of the polar equation.Describe your viewing window. $r = \frac { 7 } { 4 }$

Find the vertex, focus, and directrix of the parabola. $( x + 3 ) + ( y - 1 ) ^ { 2 } = 0$

Find the distance between the point and the line.Round your answer to four decimal places. Point Line $( 2,3 ) \quad x - y = 2$

Find the center, vertices and foci of the hyperbola. $5 x ^ { 2 } - 6 y ^ { 2 } = 30$

Convert the rectangular equation to polar form.Assume r > 1. $5 x + 7 y - 4 = 0$

Find the vertex and focus of the parabola from the given equation and select its graph. $y ^ { 2 } = 6 x$

Identify the conic. $4 y ^ { 2 } - 8 x = 0$

After a rotation of axes is used to eliminate the $x y$ -term from an equation of the form $A x ^ { 2 } + B x y + C y ^ { 2 } + D x + B y + F = 0$ the coefficients of the $x ^ { 2 }$ -and $y ^ { 2 }$ -terms remain $A$ and $C$ , respectively.

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

Find the standard form of the equation of the parabola with the given characteristics. Vertex: (6,5)( 6,5 )(6,5) ; focus: (8,5)( 8,5 )(8,5)

Determine the angle θ\thetaθ through which the axes are rotated.Round your answer to two decimal places. 17x2+72xy−3y2=7717 x ^ { 2 } + 72 x y - 3 y ^ { 2 } = 7717x2+72xy−3y2=77

Convert the rectangular equation to polar form.Assume r > 1. x=17ax = 17 ax=17a

Select the parametric equations matching with the following graph.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Directrix: y=3y = 3y=3

Find the center and vertices of the ellipse. x2+9y2+16x+18y+64=0x ^ { 2 } + 9 y ^ { 2 } + 16 x + 18 y + 64 = 0x2+9y2+16x+18y+64=0

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. Parabola: x2+20y=0x ^ { 2 } + 20 y = 0x2+20y=0 Tangent Line: x+y−5=0x + y - 5 = 0x+y−5=0

Find the vertex and focus of the parabola from the given equation and select its graph. x2+16y=0x ^ { 2 } + 16 y = 0x2+16y=0

Select the graph of degenerate conic. x2+2xy+y2−9=0x ^ { 2 } + 2 x y + y ^ { 2 } - 9 = 0x2+2xy+y2−9=0

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. r=7csc⁡θr = 7 \csc \thetar=7cscθ

Convert the rectangular equation to polar form.Assume r > 1. y=−3y = - 3y=−3

Select the correct graph of the polar equation.Describe your viewing window. r=74r = \frac { 7 } { 4 }r=47​

Find the vertex, focus, and directrix of the parabola. (x+3)+(y−1)2=0( x + 3 ) + ( y - 1 ) ^ { 2 } = 0(x+3)+(y−1)2=0

Find the distance between the point and the line.Round your answer to four decimal places. Point Line (2,3)x−y=2( 2,3 ) \quad x - y = 2(2,3)x−y=2

Find the center, vertices and foci of the hyperbola. 5x2−6y2=305 x ^ { 2 } - 6 y ^ { 2 } = 305x2−6y2=30

Convert the rectangular equation to polar form.Assume r > 1. 5x+7y−4=05 x + 7 y - 4 = 05x+7y−4=0

Find the vertex and focus of the parabola from the given equation and select its graph. y2=6xy ^ { 2 } = 6 xy2=6x

Identify the conic. 4y2−8x=04 y ^ { 2 } - 8 x = 04y2−8x=0

After a rotation of axes is used to eliminate the xyx yxy -term from an equation of the form Ax2+Bxy+Cy2+Dx+By+F=0A x ^ { 2 } + B x y + C y ^ { 2 } + D x + B y + F = 0Ax2+Bxy+Cy2+Dx+By+F=0 the coefficients of the x2x ^ { 2 }x2 -and y2y ^ { 2 }y2 -terms remain AAA and CCC , respectively.

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

Find the standard form of the equation of the parabola with the given characteristics. Vertex: $( 6,5 )$ ; focus: $( 8,5 )$

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $17 x ^ { 2 } + 72 x y - 3 y ^ { 2 } = 77$

Convert the rectangular equation to polar form.Assume r > 1. $x = 17 a$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Directrix: $y = 3$

Find the center and vertices of the ellipse. $x ^ { 2 } + 9 y ^ { 2 } + 16 x + 18 y + 64 = 0$

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. Parabola: $x ^ { 2 } + 20 y = 0$ Tangent Line: $x + y - 5 = 0$

Find the vertex and focus of the parabola from the given equation and select its graph. $x ^ { 2 } + 16 y = 0$

Select the graph of degenerate conic. $x ^ { 2 } + 2 x y + y ^ { 2 } - 9 = 0$

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. $r = 7 \csc \theta$

Convert the rectangular equation to polar form.Assume r > 1. $y = - 3$

Select the correct graph of the polar equation.Describe your viewing window. $r = \frac { 7 } { 4 }$

Find the vertex, focus, and directrix of the parabola. $( x + 3 ) + ( y - 1 ) ^ { 2 } = 0$

Find the distance between the point and the line.Round your answer to four decimal places. Point Line $( 2,3 ) \quad x - y = 2$

Find the center, vertices and foci of the hyperbola. $5 x ^ { 2 } - 6 y ^ { 2 } = 30$

Convert the rectangular equation to polar form.Assume r > 1. $5 x + 7 y - 4 = 0$

Find the vertex and focus of the parabola from the given equation and select its graph. $y ^ { 2 } = 6 x$

Identify the conic. $4 y ^ { 2 } - 8 x = 0$

After a rotation of axes is used to eliminate the $x y$ -term from an equation of the form $A x ^ { 2 } + B x y + C y ^ { 2 } + D x + B y + F = 0$ the coefficients of the $x ^ { 2 }$ -and $y ^ { 2 }$ -terms remain $A$ and $C$ , respectively.