Find a polar equation of the conic with its focus at the pole. $\begin{array} { l l l } \text { Conics } & \text { Eccentrity } & \text { Directrix } \\ \text { Parabola } & e = 1 & x = - 4 \end{array}$

A) $r = \frac { 4 } { 1 - \sin \theta }$ B) $r = \frac { 4 } { 1 - \cos \theta }$ C) $r = \frac { - 4 } { 1 - \cos \theta }$ D) $r = \frac { 4 } { 1 + \sin \theta }$ E) $r = \frac { 4 } { 1 + \cos \theta }$ A) $r = \frac { 4 } { 1 - \sin \theta }$ B) $r = \frac { 4 } { 1 - \cos \theta }$ C) $r = \frac { - 4 } { 1 - \cos \theta }$ D) $r = \frac { 4 } { 1 + \sin \theta }$ E) $r = \frac { 4 } { 1 + \cos \theta }$

Exam 10: Topics In Analytic Geometry

A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. $A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. a = 6 , b = \frac { \pi } { 2 }$ $a = 6 , b = \frac { \pi } { 2 }$

(Multiple Choice)

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Question 21

Write the equation of the circle graphed below.Express the equation in standard form.

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Question 22

A moving conveyor is built so that it rises 3 meter for each 5 meters of horizontal travel.The conveyor runs between two floors in a factory.The distance between the floors is 4 meters.Find the length of the conveyor.Round your answers to one decimal place.

(Multiple Choice)

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Question 23

Select the graph of $r = 4 \cos \theta$ over the interval.Describe the part of the graph obtained in this case. $\frac { \pi } { 4 } \leq \theta \leq \frac { 3 \pi } { 4 }$

(Multiple Choice)

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Question 24

Convert the polar equation to rectangular form. $r = 6 \cos 2 \theta$

(Multiple Choice)

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Question 25

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 3 - 5 \sin \theta$

(Multiple Choice)

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Question 26

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (±3,0); passes through the point $( 5 , \sqrt { 3 } )$

(Multiple Choice)

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Question 27

Select the curve represented by the parametric equations. Prolate cycloid: $x = 3 \Theta - 7 \sin \Theta , y = 3 - 7 \cos \Theta$

(Multiple Choice)

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Question 28

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

(Multiple Choice)

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Question 29

Find the vertex and focus of the parabola. $x ^ { 2 } + 8 y = 0$

(Multiple Choice)

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Question 30

A point in rectangular coordinates is given.Convert the point to polar coordinates.Round your answers to two decimal places, r > 0. $( 11,13 )$

(Multiple Choice)

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Question 31

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Eccentricity $\quad$ $\quad$ Directrix Ellipse $\quad\quad\quad e = \frac { 1 } { 2 } \quad\quad\quad y = -3$

(Multiple Choice)

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Question 32

Select the graph of the equation. $r = - 4 \sec \theta$

(Multiple Choice)

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Question 33

Find a polar equation of the conic with its focus at the pole. Conics Eccentrity Directrix Parabola e=1 x=-4

(Multiple Choice)

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Question 34

A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 20 feet and a height at the center of 4 feet.Select the arch of the tunnel on a rectangular coordinate system with the center of the road entering the tunnel at the origin.Identify the coordinates of the known points.

(Multiple Choice)

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Question 35

Select the graph of the following equation $36 x ^ { 2 } + 72 x y + 36 y ^ { 2 } = 0$

(Multiple Choice)

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Question 36

Convert the rectangular equation to polar form.Assume r > 1. $y = 6$

(Multiple Choice)

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Question 37

Any sound from one focus of an ellipse reflects off the ellipse directly back to the other focus.This property explains whispering galleries such as Statuary Hall in Washington, D.C.The whispering gallery shown in illustration has the shape of a semi-circle.Find the distance sound travels as it leaves focus F and returns to focus F'.Round your answer to one decimal place, if necessary.

(Multiple Choice)

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Question 38

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=52\Theta y=52\theta

(Multiple Choice)

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Question 39

Convert the polar equation to rectangular form. $r = - 9 \sec \theta$

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Question 40

A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. $A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. a = 6 , b = \frac { \pi } { 2 }$ $a = 6 , b = \frac { \pi } { 2 }$

Write the equation of the circle graphed below.Express the equation in standard form.

A moving conveyor is built so that it rises 3 meter for each 5 meters of horizontal travel.The conveyor runs between two floors in a factory.The distance between the floors is 4 meters.Find the length of the conveyor.Round your answers to one decimal place.

Select the graph of $r = 4 \cos \theta$ over the interval.Describe the part of the graph obtained in this case. $\frac { \pi } { 4 } \leq \theta \leq \frac { 3 \pi } { 4 }$

Convert the polar equation to rectangular form. $r = 6 \cos 2 \theta$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 3 - 5 \sin \theta$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (±3,0); passes through the point $( 5 , \sqrt { 3 } )$

Select the curve represented by the parametric equations. Prolate cycloid: $x = 3 \Theta - 7 \sin \Theta , y = 3 - 7 \cos \Theta$

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

Find the vertex and focus of the parabola. $x ^ { 2 } + 8 y = 0$

A point in rectangular coordinates is given.Convert the point to polar coordinates.Round your answers to two decimal places, r > 0. $( 11,13 )$

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Eccentricity $\quad$ $\quad$ Directrix Ellipse $\quad\quad\quad e = \frac { 1 } { 2 } \quad\quad\quad y = -3$

Select the graph of the equation. $r = - 4 \sec \theta$

Find a polar equation of the conic with its focus at the pole. Conics Eccentrity Directrix Parabola e=1 x=-4

Select the graph of the following equation $36 x ^ { 2 } + 72 x y + 36 y ^ { 2 } = 0$

Convert the rectangular equation to polar form.Assume r > 1. $y = 6$

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=52\Theta y=52\theta

Convert the polar equation to rectangular form. $r = - 9 \sec \theta$

Functions and Their Graphs

Polynomial and Rational Functions

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Trigonometry

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Limits and An Introduction To Calculus

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Exam 10: Topics In Analytic Geometry

A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. a=6,b=π2a = 6 , b = \frac { \pi } { 2 }a=6,b=2π​

Write the equation of the circle graphed below.Express the equation in standard form.

A moving conveyor is built so that it rises 3 meter for each 5 meters of horizontal travel.The conveyor runs between two floors in a factory.The distance between the floors is 4 meters.Find the length of the conveyor.Round your answers to one decimal place.

Select the graph of r=4cos⁡θr = 4 \cos \thetar=4cosθ over the interval.Describe the part of the graph obtained in this case. π4≤θ≤3π4\frac { \pi } { 4 } \leq \theta \leq \frac { 3 \pi } { 4 }4π​≤θ≤43π​

Convert the polar equation to rectangular form. r=6cos⁡2θr = 6 \cos 2 \thetar=6cos2θ

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=3−5sin⁡θr = 3 - 5 \sin \thetar=3−5sinθ

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (±3,0); passes through the point (5,3)( 5 , \sqrt { 3 } )(5,3​)

Select the curve represented by the parametric equations. Prolate cycloid: x=3Θ−7sin⁡Θ,y=3−7cos⁡Θx = 3 \Theta - 7 \sin \Theta , y = 3 - 7 \cos \Thetax=3Θ−7sinΘ,y=3−7cosΘ

Find the vertex, focus, and directrix of the parabola. y=−3x2y = - 3 x ^ { 2 }y=−3x2

Find the vertex and focus of the parabola. x2+8y=0x ^ { 2 } + 8 y = 0x2+8y=0

A point in rectangular coordinates is given.Convert the point to polar coordinates.Round your answers to two decimal places, r > 0. (11,13)( 11,13 )(11,13)

Find a polar equation of the conic with its focus at the pole. Conics \quad\quad Eccentricity \quad\quad Directrix Ellipse e=12y=−3\quad\quad\quad e = \frac { 1 } { 2 } \quad\quad\quad y = -3e=21​y=−3

Select the graph of the equation. r=−4sec⁡θr = - 4 \sec \thetar=−4secθ

Find a polar equation of the conic with its focus at the pole. Conics Eccentrity Directrix Parabola e=1 x=-4

Select the graph of the following equation 36x2+72xy+36y2=036 x ^ { 2 } + 72 x y + 36 y ^ { 2 } = 036x2+72xy+36y2=0

Convert the rectangular equation to polar form.Assume r > 1. y=6y = 6y=6

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=52\Theta y=52\theta

Convert the polar equation to rectangular form. r=−9sec⁡θr = - 9 \sec \thetar=−9secθ

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

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A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. $A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. a = 6 , b = \frac { \pi } { 2 }$ $a = 6 , b = \frac { \pi } { 2 }$

Select the graph of $r = 4 \cos \theta$ over the interval.Describe the part of the graph obtained in this case. $\frac { \pi } { 4 } \leq \theta \leq \frac { 3 \pi } { 4 }$

Convert the polar equation to rectangular form. $r = 6 \cos 2 \theta$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 3 - 5 \sin \theta$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (±3,0); passes through the point $( 5 , \sqrt { 3 } )$

Select the curve represented by the parametric equations. Prolate cycloid: $x = 3 \Theta - 7 \sin \Theta , y = 3 - 7 \cos \Theta$

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

Find the vertex and focus of the parabola. $x ^ { 2 } + 8 y = 0$

A point in rectangular coordinates is given.Convert the point to polar coordinates.Round your answers to two decimal places, r > 0. $( 11,13 )$

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Eccentricity $\quad$ $\quad$ Directrix Ellipse $\quad\quad\quad e = \frac { 1 } { 2 } \quad\quad\quad y = -3$

Select the graph of the equation. $r = - 4 \sec \theta$

Select the graph of the following equation $36 x ^ { 2 } + 72 x y + 36 y ^ { 2 } = 0$

Convert the rectangular equation to polar form.Assume r > 1. $y = 6$

Convert the polar equation to rectangular form. $r = - 9 \sec \theta$