Question 1

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

Accepted Answer

A) vertex: (0,0) focus: $\left( - \frac { 9 } { 8 } , 0 \right)$ 
B) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( - \frac { 9 } { 2 } , - \frac { 9 } { 2 } \right)$ 
C) vertex: (0,0) focus: $\left( 0 , - \frac { 9 } { 2 } \right)$ 
D) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( 0 , - \frac { 9 } { 8 } \right)$ 
E) vertex: (0,0) focus: $\left( - \frac { 9 } { 2 } , 0 \right)$ 
A) vertex: (0,0) focus: $\left( - \frac { 9 } { 8 } , 0 \right)$ 
B) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( - \frac { 9 } { 2 } , - \frac { 9 } { 2 } \right)$ 
C) vertex: (0,0) focus: $\left( 0 , - \frac { 9 } { 2 } \right)$ 
D) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( 0 , - \frac { 9 } { 8 } \right)$ 
E) vertex: (0,0) focus: $\left( - \frac { 9 } { 2 } , 0 \right)$

Question 2

Select the polar equation of graph.

Accepted Answer

A)  $\frac { 6 } { 2 - \cos \theta }$ 
B)  $\frac { 6 } { 2 - \sin \theta }$ 
C)  $\frac { 1 } { 2 - \cos \theta }$ 
D)  $\frac { 6 } { 2 + \sin \theta }$ 
E)  $\frac { 6 } { 2 + \cos \theta }$ 
A)  $\frac { 6 } { 2 - \cos \theta }$ 
B)  $\frac { 6 } { 2 - \sin \theta }$ 
C)  $\frac { 1 } { 2 - \cos \theta }$ 
D)  $\frac { 6 } { 2 + \sin \theta }$ 
E)  $\frac { 6 } { 2 + \cos \theta }$

Question 3

Select the curve represented by the parametric equations. 
Curtate cycloid: $x = 4 \Theta - 2 \sin \Theta , y = 4 - 2 \cos \Theta$

Accepted Answer

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

Question 4

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $r = \frac { 8 } { 2 \sin \theta - 3 \cos \theta }$

Accepted Answer

A)  $y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$    
B)  $y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$    
C)  $y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$    
D)  $y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$    
E)  $y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$    
A)  $y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$    
B)  $y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$    
C)  $y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$    
D)  $y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$    
E)  $y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$

Question 5

Find the standard form of the equation of the ellipse with the following characteristics. focies: (±8,0) major axis of length: 22

Accepted Answer

A)  $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 64 } = 1$ 
C)  $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 57 } = 1$ 
D)  $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 420 } = 1$ 
E)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 121 } = 1$ 
A)  $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 64 } = 1$ 
C)  $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 57 } = 1$ 
D)  $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 420 } = 1$ 
E)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 121 } = 1$

Question 6

Find a polar equation of the conic with its focus at the pole. 
Conics$\quad$$\quad$Vertex or vertices
Parabola$\quad$$\quad$$( 6 , \pi )$

Accepted Answer

A)  $\frac { 12 } { 1 + \cos \theta }$ 
B)  $\frac { - 12 } { 1 - \sin \theta }$ 
C)  $\frac { 12 } { 1 + \sin \theta }$ 
D)  $\frac { 12 } { 1 - \sin \theta }$ 
E)  $\frac { 12 } { 1 - \cos \theta }$ 
A)  $\frac { 12 } { 1 + \cos \theta }$ 
B)  $\frac { - 12 } { 1 - \sin \theta }$ 
C)  $\frac { 12 } { 1 + \sin \theta }$ 
D)  $\frac { 12 } { 1 - \sin \theta }$ 
E)  $\frac { 12 } { 1 - \cos \theta }$

Question 7

Using following result find a set of parametric equation of conic.  $x = h + a \cos \theta , y = k + b i s n \theta$ 
Vertices: $( \pm 17,0 )$ ; foci: $( \pm 15,0 )$

Accepted Answer

A)  $x = 8 \cos \theta , y = 17 \sin \theta$ 
B)  $x = 15 + 17 \cos \theta , y = 15 - 8 \sin \theta$ 
C)  $x = 8 - 15 \cos \theta , y = 17 + 15 \sin \theta$ 
D)  $x = 15 - 17 \cos \theta , y = 8 \sin \theta$ 
E)  $x = 17 \cos \theta , y = 8 \sin \theta$ 
A)  $x = 8 \cos \theta , y = 17 \sin \theta$ 
B)  $x = 15 + 17 \cos \theta , y = 15 - 8 \sin \theta$ 
C)  $x = 8 - 15 \cos \theta , y = 17 + 15 \sin \theta$ 
D)  $x = 15 - 17 \cos \theta , y = 8 \sin \theta$ 
E)  $x = 17 \cos \theta , y = 8 \sin \theta$

Question 8

Find the standard form of the equation of the ellipse with the following characteristics. 
Foci: $( \pm 5,0 )$ , major axis of length: 18

Accepted Answer

A)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 56 } = 1$ 
B)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 81 } = 1$ 
D)  $\frac { x ^ { 2 } } { 324 } + \frac { y ^ { 2 } } { 25 } = 1$ 
E)  $\frac { x ^ { 2 } } { 324 } + \frac { y ^ { 2 } } { 299 } = 1$ 
A)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 56 } = 1$ 
B)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 81 } = 1$ 
D)  $\frac { x ^ { 2 } } { 324 } + \frac { y ^ { 2 } } { 25 } = 1$ 
E)  $\frac { x ^ { 2 } } { 324 } + \frac { y ^ { 2 } } { 299 } = 1$

Question 9

Using following result find a set of parametric equation of conic. 
Circle: $x = h + r \cos \theta , y = k + r \sin \theta$ 
Circle: center: $( 2,6 )$ ; radius: 8

Accepted Answer

A)  $x = 6 + 8 \cos \theta , y = 6 + 2 \sin \theta$ 
B)  $x = 2 + 6 \cos \theta , y = 6 + 8 \sin \theta$ 
C)  $x = 2 + 8 \cos \theta , y = 6 + 8 \sin \theta$ 
D)  $x = 8 + 2 \cos \theta , y = 6 + 2 \sin \theta$ 
E)  $x = 8 + 6 \cos \theta , y = 6 + 2 \sin \theta$ 
A)  $x = 6 + 8 \cos \theta , y = 6 + 2 \sin \theta$ 
B)  $x = 2 + 6 \cos \theta , y = 6 + 8 \sin \theta$ 
C)  $x = 2 + 8 \cos \theta , y = 6 + 8 \sin \theta$ 
D)  $x = 8 + 2 \cos \theta , y = 6 + 2 \sin \theta$ 
E)  $x = 8 + 6 \cos \theta , y = 6 + 2 \sin \theta$

Question 10

Find a polar equation of the conic with its focus at the pole. 
Conics $\quad$$\quad$$\quad$Vertex or vertices
Parabola $\quad$$\quad ( 1 , - \pi / 2 )$

Accepted Answer

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

Question 11

Convert the polar equation to rectangular form.  $r = 4 \csc \theta$

Accepted Answer

A)  $y = 4$ 
B)  $y = 4 \mathrm { r }$ 
C)  $x = 4$ 
D)  $6 y = \mathrm { r }$ 
E)  $x = 4 \mathrm { r }$ 
A)  $y = 4$ 
B)  $y = 4 \mathrm { r }$ 
C)  $x = 4$ 
D)  $6 y = \mathrm { r }$ 
E)  $x = 4 \mathrm { r }$

Question 12

Identify the conic.  $4 y ^ { 2 } + 5 x ^ { 2 } - 20 = 0$

Accepted Answer

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

Question 13

Find the standard form of the equation of the hyperbola with the given characteristics. 
vertices: (5, -6), (5, -2)
Foci: (5, -7), (5, -1)

Accepted Answer

A)  $\frac { ( y + 4 ) ^ { 2 } } { 4 } - \frac { ( x - 5 ) ^ { 2 } } { 5 } = 1$ 
B)  $\frac { ( y + 4 ) ^ { 2 } } { 4 } + \frac { ( x - 5 ) ^ { 2 } } { 5 } = 1$ 
C)  $\frac { ( y - 5 ) ^ { 2 } } { 4 } - \frac { ( x + 4 ) ^ { 2 } } { 5 } = 1$ 
D)  $\frac { ( y + 5 ) ^ { 2 } } { 4 } - \frac { ( x - 4 ) ^ { 2 } } { 5 } = 1$ 
E)  $\frac { ( y - 4 ) ^ { 2 } } { 4 } - \frac { ( x + 5 ) ^ { 2 } } { 9 } = 1$ 
A)  $\frac { ( y + 4 ) ^ { 2 } } { 4 } - \frac { ( x - 5 ) ^ { 2 } } { 5 } = 1$ 
B)  $\frac { ( y + 4 ) ^ { 2 } } { 4 } + \frac { ( x - 5 ) ^ { 2 } } { 5 } = 1$ 
C)  $\frac { ( y - 5 ) ^ { 2 } } { 4 } - \frac { ( x + 4 ) ^ { 2 } } { 5 } = 1$ 
D)  $\frac { ( y + 5 ) ^ { 2 } } { 4 } - \frac { ( x - 4 ) ^ { 2 } } { 5 } = 1$ 
E)  $\frac { ( y - 4 ) ^ { 2 } } { 4 } - \frac { ( x + 5 ) ^ { 2 } } { 9 } = 1$

Question 14

Find the standard form of the equation of the parabola with the given characteristics. 
Vertex: $( - 5,5 )$ ; focus: $( - 5,0 )$

Accepted Answer

A)  $( x - 5 ) ^ { 2 } = 20 ( y - 5 )$ 
B)  $( x - 5 ) ^ { 2 } = - 20 ( y - 5 )$ 
C)  $( y - 5 ) ^ { 2 } = - 20 ( x - 5 )$ 
D)  $( y - 5 ) ^ { 2 } = 20 ( x - 5 )$ 
E)  $( x + 5 ) ^ { 2 } = - 20 ( y - 5 )$ 
A)  $( x - 5 ) ^ { 2 } = 20 ( y - 5 )$ 
B)  $( x - 5 ) ^ { 2 } = - 20 ( y - 5 )$ 
C)  $( y - 5 ) ^ { 2 } = - 20 ( x - 5 )$ 
D)  $( y - 5 ) ^ { 2 } = 20 ( x - 5 )$ 
E)  $( x + 5 ) ^ { 2 } = - 20 ( y - 5 )$

Question 15

Select the graph for following equation.  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$

Accepted Answer

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

Question 16

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

Accepted Answer

A)    Lower half of circle 
B)   Lower half of circle 
C)   Lower half of circle 
D)    Lower half of circle 
E)   Lower half of circle 
A)    Lower half of circle 
B)   Lower half of circle 
C)   Lower half of circle 
D)    Lower half of circle 
E)   Lower half of circle

Question 17

Find the standard form of the equation of the ellipse with the given characteristics. 
Center: $( - 6,4 )$ , a = 5c, foci: $( - 8,4 ) , ( - 4,4 )$ , where a - thr semimajor axis, b - semiminor axis and $c ^ { 2 } = a ^ { 2 } - b ^ { 2 }$ .

Accepted Answer

A)  $\frac { ( x - 6 ) ^ { 2 } } { 96 } + \frac { ( y + 4 ) ^ { 2 } } { 100 } = 1$ 
B)  $\frac { ( x + 6 ) ^ { 2 } } { 96 } + \frac { ( y - 4 ) ^ { 2 } } { 100 } = 1$ 
C)  $\frac { ( x + 6 ) ^ { 2 } } { 100 } + \frac { ( y - 4 ) ^ { 2 } } { 96 } = 1$ 
D)  $\frac { ( x - 4 ) ^ { 2 } } { 100 } + \frac { ( y + 6 ) ^ { 2 } } { 96 } = 1$ 
E)  $\frac { ( x + 4 ) ^ { 2 } } { 100 } + \frac { ( y - 6 ) ^ { 2 } } { 96 } = 1$ 
A)  $\frac { ( x - 6 ) ^ { 2 } } { 96 } + \frac { ( y + 4 ) ^ { 2 } } { 100 } = 1$ 
B)  $\frac { ( x + 6 ) ^ { 2 } } { 96 } + \frac { ( y - 4 ) ^ { 2 } } { 100 } = 1$ 
C)  $\frac { ( x + 6 ) ^ { 2 } } { 100 } + \frac { ( y - 4 ) ^ { 2 } } { 96 } = 1$ 
D)  $\frac { ( x - 4 ) ^ { 2 } } { 100 } + \frac { ( y + 6 ) ^ { 2 } } { 96 } = 1$ 
E)  $\frac { ( x + 4 ) ^ { 2 } } { 100 } + \frac { ( y - 6 ) ^ { 2 } } { 96 } = 1$

Question 18

In a suspension bridge, the shape of the suspension cables is parabolic.The bridge shown in the figure has towers that are 1000 m apart, and the lowest point of the suspension cables is 200 m below the top of the towers.Find the equation of the parabolic part of the cables, placing the origin of the coordinate system at the lowest point of the cable. ​
NOTE: This equation is used to find the length of the cable needed in the construction of the bridge.
​   ​

Accepted Answer

A) x 2 = 2,500y 
B) y 2 = 5,000x 
C) x 2 = 1,250y 
D) x 2 = 5,000y 
E) x 2 = -1,250y 
A) x 2 = 2,500y 
B) y 2 = 5,000x 
C) x 2 = 1,250y 
D) x 2 = 5,000y 
E) x 2 = -1,250y

Question 19

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. 
Focus: $\left( - \frac { 7 } { 2 } , 0 \right)$

Accepted Answer

A)  $x ^ { 2 } = 14 y$ 
B)  $y ^ { 2 } = - 14 x$ 
C)  $y ^ { 2 } = 14 x$ 
D)  $x ^ { 2 } = - 14 y$ 
E)  $y ^ { 2 } = - \frac { x } { 14 }$ 
A)  $x ^ { 2 } = 14 y$ 
B)  $y ^ { 2 } = - 14 x$ 
C)  $y ^ { 2 } = 14 x$ 
D)  $x ^ { 2 } = - 14 y$ 
E)  $y ^ { 2 } = - \frac { x } { 14 }$

Question 20

Use the discriminant to classify the graph.  $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 72 = 0$

Accepted Answer

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

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

Select the polar equation of graph.

Select the curve represented by the parametric equations. Curtate cycloid: $x = 4 \Theta - 2 \sin \Theta , y = 4 - 2 \cos \Theta$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = \frac { 8 } { 2 \sin \theta - 3 \cos \theta }$

Find the standard form of the equation of the ellipse with the following characteristics. focies: (±8,0) major axis of length: 22

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Vertex or vertices Parabola $\quad$ $\quad$ $( 6 , \pi )$

Using following result find a set of parametric equation of conic. $x = h + a \cos \theta , y = k + b i s n \theta$ Vertices: $( \pm 17,0 )$ ; foci: $( \pm 15,0 )$

Find the standard form of the equation of the ellipse with the following characteristics. Foci: $( \pm 5,0 )$ , major axis of length: 18

Using following result find a set of parametric equation of conic. Circle: $x = h + r \cos \theta , y = k + r \sin \theta$ Circle: center: $( 2,6 )$ ; radius: 8

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ $\quad$ Vertex or vertices Parabola $\quad$ $\quad ( 1 , - \pi / 2 )$

Convert the polar equation to rectangular form. $r = 4 \csc \theta$

Identify the conic. $4 y ^ { 2 } + 5 x ^ { 2 } - 20 = 0$

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (5, -6), (5, -2) Foci: (5, -7), (5, -1)

Find the standard form of the equation of the parabola with the given characteristics. Vertex: $( - 5,5 )$ ; focus: $( - 5,0 )$

Select the graph for following equation. $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$

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

Find the standard form of the equation of the ellipse with the given characteristics. Center: $( - 6,4 )$ , a = 5c, foci: $( - 8,4 ) , ( - 4,4 )$ , where a - thr semimajor axis, b - semiminor axis and $c ^ { 2 } = a ^ { 2 } - b ^ { 2 }$ .

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Focus: $\left( - \frac { 7 } { 2 } , 0 \right)$

Use the discriminant to classify the graph. $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 72 = 0$

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

Find the vertex and focus of the parabola. y2=−92xy ^ { 2 } = - \frac { 9 } { 2 } xy2=−29​x

Select the polar equation of graph.

Select the curve represented by the parametric equations. Curtate cycloid: x=4Θ−2sin⁡Θ,y=4−2cos⁡Θx = 4 \Theta - 2 \sin \Theta , y = 4 - 2 \cos \Thetax=4Θ−2sinΘ,y=4−2cosΘ

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=82sin⁡θ−3cos⁡θr = \frac { 8 } { 2 \sin \theta - 3 \cos \theta }r=2sinθ−3cosθ8​

Find the standard form of the equation of the ellipse with the following characteristics. focies: (±8,0) major axis of length: 22

Find a polar equation of the conic with its focus at the pole. Conics \quad\quad Vertex or vertices Parabola \quad\quad(6,π)( 6 , \pi )(6,π)

Using following result find a set of parametric equation of conic. x=h+acos⁡θ,y=k+bisnθx = h + a \cos \theta , y = k + b i s n \thetax=h+acosθ,y=k+bisnθ Vertices: (±17,0)( \pm 17,0 )(±17,0) ; foci: (±15,0)( \pm 15,0 )(±15,0)

Find the standard form of the equation of the ellipse with the following characteristics. Foci: (±5,0)( \pm 5,0 )(±5,0) , major axis of length: 18

Using following result find a set of parametric equation of conic. Circle: x=h+rcos⁡θ,y=k+rsin⁡θx = h + r \cos \theta , y = k + r \sin \thetax=h+rcosθ,y=k+rsinθ Circle: center: (2,6)( 2,6 )(2,6) ; radius: 8

Find a polar equation of the conic with its focus at the pole. Conics \quad\quad\quad Vertex or vertices Parabola \quad(1,−π/2)\quad ( 1 , - \pi / 2 )(1,−π/2)

Convert the polar equation to rectangular form. r=4csc⁡θr = 4 \csc \thetar=4cscθ

Identify the conic. 4y2+5x2−20=04 y ^ { 2 } + 5 x ^ { 2 } - 20 = 04y2+5x2−20=0

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (5, -6), (5, -2) Foci: (5, -7), (5, -1)

Find the standard form of the equation of the parabola with the given characteristics. Vertex: (−5,5)( - 5,5 )(−5,5) ; focus: (−5,0)( - 5,0 )(−5,0)

Select the graph for following equation. x225+y216=1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 125x2​+16y2​=1

Select the graph of r=3cos⁡θr = 3 \cos \thetar=3cosθ over the interval.Describe the part of the graph obtained in this case. π2≤θ≤π\frac { \pi } { 2 } \leq \theta \leq \pi2π​≤θ≤π

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Focus: (−72,0)\left( - \frac { 7 } { 2 } , 0 \right)(−27​,0)

Use the discriminant to classify the graph. 5x2+10xy+11y2+9x−10y−72=05 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 72 = 05x2+10xy+11y2+9x−10y−72=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

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

Select the curve represented by the parametric equations. Curtate cycloid: $x = 4 \Theta - 2 \sin \Theta , y = 4 - 2 \cos \Theta$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = \frac { 8 } { 2 \sin \theta - 3 \cos \theta }$

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Vertex or vertices Parabola $\quad$ $\quad$ $( 6 , \pi )$

Using following result find a set of parametric equation of conic. $x = h + a \cos \theta , y = k + b i s n \theta$ Vertices: $( \pm 17,0 )$ ; foci: $( \pm 15,0 )$

Find the standard form of the equation of the ellipse with the following characteristics. Foci: $( \pm 5,0 )$ , major axis of length: 18

Using following result find a set of parametric equation of conic. Circle: $x = h + r \cos \theta , y = k + r \sin \theta$ Circle: center: $( 2,6 )$ ; radius: 8

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ $\quad$ Vertex or vertices Parabola $\quad$ $\quad ( 1 , - \pi / 2 )$

Convert the polar equation to rectangular form. $r = 4 \csc \theta$

Identify the conic. $4 y ^ { 2 } + 5 x ^ { 2 } - 20 = 0$

Find the standard form of the equation of the parabola with the given characteristics. Vertex: $( - 5,5 )$ ; focus: $( - 5,0 )$

Select the graph for following equation. $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$

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

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Focus: $\left( - \frac { 7 } { 2 } , 0 \right)$

Use the discriminant to classify the graph. $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 72 = 0$