Exam 10: Analytic Geometry

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the sum of the distances from the points $( 2,0 )$ and $( - 2,0 )$ is 21 .

(Multiple Choice)

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Question 41

Write an equation for the ellipse. -foci at $( \pm 6,0 ) ; x$ -intercepts $\pm 10$

(Multiple Choice)

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Question 42

Write an equation for the parabola with vertex at the origin. -Focus $( 0 , - 3 )$

(Multiple Choice)

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Question 43

Write an equation for the parabola. -vertex $( - 6 , - 7 )$ , focus $( - 6 , - 11 )$

(Multiple Choice)

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Question 44

Graph the conic section. -

(Multiple Choice)

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Question 45

Write an equation for the ellipse. -eccentricity $\frac { 3 } { 5 }$ ; vertices at $( 0 , - 5 ) , ( 0,5 )$

(Multiple Choice)

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Question 46

Solve the problem. -The roof of a building is in the shape of the hyperbola $3 \mathrm { y } ^ { 2 } - \mathrm { x } ^ { 2 } = 5$ , where $\mathrm { x }$ and $\mathrm { y }$ are in meters. Refer to the figure and determine the height, $h$ , of the outside walls. $\mathrm { A } = 7 \mathrm {~m}$ $Solve the problem. -The roof of a building is in the shape of the hyperbola 3 \mathrm { y } ^ { 2 } - \mathrm { x } ^ { 2 } = 5 , where \mathrm { x } and \mathrm { y } are in meters. Refer to the figure and determine the height, h , of the outside walls. \mathrm { A } = 7 \mathrm {~m}$

(Multiple Choice)

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Question 47

Write an equation for the parabola with vertex at the origin. -Through $( 3 , - 3 \sqrt { 3 } )$ , symmetric with respect to the $x$ -axis

(Multiple Choice)

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Question 48

Write an equation for the parabola. -vertex $( 3 , - 7 )$ , focus $( 3 , - 2 )$

(Multiple Choice)

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Question 49

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $4 x ^ { 2 } = 16 - 4 y ^ { 2 }$

(Multiple Choice)

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Question 50

Write an equation for the hyperbola. -foci at $( 6 - 2 \sqrt { 29 } , 9 ) , ( 6 + 2 \sqrt { 29 } , 9 )$ ; eccentricity $\frac { 2 \sqrt { 29 } } { 10 }$

(Multiple Choice)

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Question 51

Write the word or phrase that best completes each statement or answers the question. -Explain the differences between an ellipse and a hyperbola. Both definitions emphasize distance, but how is distance used differently in these two definitions?

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Question 52

Write the word or phrase that best completes each statement or answers the question. - $36 \mathrm { y } ^ { 2 } = 576 - 4 \mathrm { x } ^ { 2 }$

(Multiple Choice)

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Question 53

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x = 8 y ^ { 2 } - 5 y + 7$

(Multiple Choice)

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Question 54

Write an equation for the parabola with vertex at the origin. -Through $( - 2,2 )$ , opening to the left

(Multiple Choice)

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Question 55

Write an equation for the hyperbola. -center at $( 1 , - 8 ) ;$ focus at $( 1 - 2 \sqrt { 17 } , - 8 ) ;$ eccentricity $\frac { 2 \sqrt { 17 } } { 8 }$

(Multiple Choice)

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Question 56

Solve the problem. -A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 9 m down from the top of the dome the ceiling is 8 m wide, Find the best location for the light source.

(Multiple Choice)

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Question 57

Solve the problem. -A projectile is thrown upward so that its distance above the ground after $t$ seconds is $h = - 14 t ^ { 2 } + 560 \mathrm { t }$ . After how many seconds does it reach its maximum height?

(Multiple Choice)

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Question 58

Find the eccentricity of the ellipse. - $x ^ { 2 } + 25 y ^ { 2 } = 25$

(Multiple Choice)

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Question 59

Graph the ellipse. - $4(x-2)^{2}+9(y+1)^{2}=36$ $Graph the ellipse. - 4(x-2)^{2}+9(y+1)^{2}=36$

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Question 60

Showing 41 - 60 of 206

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the sum of the distances from the points $( 2,0 )$ and $( - 2,0 )$ is 21 .

Write an equation for the ellipse. -foci at $( \pm 6,0 ) ; x$ -intercepts $\pm 10$

Write an equation for the parabola with vertex at the origin. -Focus $( 0 , - 3 )$

Write an equation for the parabola. -vertex $( - 6 , - 7 )$ , focus $( - 6 , - 11 )$

Graph the conic section. -

Write an equation for the ellipse. -eccentricity $\frac { 3 } { 5 }$ ; vertices at $( 0 , - 5 ) , ( 0,5 )$

Write an equation for the parabola with vertex at the origin. -Through $( 3 , - 3 \sqrt { 3 } )$ , symmetric with respect to the $x$ -axis

Write an equation for the parabola. -vertex $( 3 , - 7 )$ , focus $( 3 , - 2 )$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $4 x ^ { 2 } = 16 - 4 y ^ { 2 }$

Write an equation for the hyperbola. -foci at $( 6 - 2 \sqrt { 29 } , 9 ) , ( 6 + 2 \sqrt { 29 } , 9 )$ ; eccentricity $\frac { 2 \sqrt { 29 } } { 10 }$

Write the word or phrase that best completes each statement or answers the question. -Explain the differences between an ellipse and a hyperbola. Both definitions emphasize distance, but how is distance used differently in these two definitions?

Write the word or phrase that best completes each statement or answers the question. - $36 \mathrm { y } ^ { 2 } = 576 - 4 \mathrm { x } ^ { 2 }$

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x = 8 y ^ { 2 } - 5 y + 7$

Write an equation for the parabola with vertex at the origin. -Through $( - 2,2 )$ , opening to the left

Write an equation for the hyperbola. -center at $( 1 , - 8 ) ;$ focus at $( 1 - 2 \sqrt { 17 } , - 8 ) ;$ eccentricity $\frac { 2 \sqrt { 17 } } { 8 }$

Solve the problem. -A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 9 m down from the top of the dome the ceiling is 8 m wide, Find the best location for the light source.

Solve the problem. -A projectile is thrown upward so that its distance above the ground after $t$ seconds is $h = - 14 t ^ { 2 } + 560 \mathrm { t }$ . After how many seconds does it reach its maximum height?

Find the eccentricity of the ellipse. - $x ^ { 2 } + 25 y ^ { 2 } = 25$

Graph the ellipse. - $4(x-2)^{2}+9(y+1)^{2}=36$ $Graph the ellipse. - 4(x-2)^{2}+9(y+1)^{2}=36$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

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Exam 10: Analytic Geometry

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the sum of the distances from the points (2,0)( 2,0 )(2,0) and (−2,0)( - 2,0 )(−2,0) is 21 .

Write an equation for the ellipse. -foci at (±6,0);x( \pm 6,0 ) ; x(±6,0);x -intercepts ±10\pm 10±10

Write an equation for the parabola with vertex at the origin. -Focus (0,−3)( 0 , - 3 )(0,−3)

Write an equation for the parabola. -vertex (−6,−7)( - 6 , - 7 )(−6,−7) , focus (−6,−11)( - 6 , - 11 )(−6,−11)

Graph the conic section. -

Write an equation for the ellipse. -eccentricity 35\frac { 3 } { 5 }53​ ; vertices at (0,−5),(0,5)( 0 , - 5 ) , ( 0,5 )(0,−5),(0,5)

Write an equation for the parabola with vertex at the origin. -Through (3,−33)( 3 , - 3 \sqrt { 3 } )(3,−33​) , symmetric with respect to the xxx -axis

Write an equation for the parabola. -vertex (3,−7)( 3 , - 7 )(3,−7) , focus (3,−2)( 3 , - 2 )(3,−2)

Identify the equation as a parabola, circle, ellipse, or hyperbola. - 4x2=16−4y24 x ^ { 2 } = 16 - 4 y ^ { 2 }4x2=16−4y2

Write an equation for the hyperbola. -foci at (6−229,9),(6+229,9)( 6 - 2 \sqrt { 29 } , 9 ) , ( 6 + 2 \sqrt { 29 } , 9 )(6−229​,9),(6+229​,9) ; eccentricity 22910\frac { 2 \sqrt { 29 } } { 10 }10229​​

Write the word or phrase that best completes each statement or answers the question. -Explain the differences between an ellipse and a hyperbola. Both definitions emphasize distance, but how is distance used differently in these two definitions?

Write the word or phrase that best completes each statement or answers the question. - 36y2=576−4x236 \mathrm { y } ^ { 2 } = 576 - 4 \mathrm { x } ^ { 2 }36y2=576−4x2

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - x=8y2−5y+7x = 8 y ^ { 2 } - 5 y + 7x=8y2−5y+7

Write an equation for the parabola with vertex at the origin. -Through (−2,2)( - 2,2 )(−2,2) , opening to the left

Write an equation for the hyperbola. -center at (1,−8);( 1 , - 8 ) ;(1,−8); focus at (1−217,−8);( 1 - 2 \sqrt { 17 } , - 8 ) ;(1−217​,−8); eccentricity 2178\frac { 2 \sqrt { 17 } } { 8 }8217​​

Solve the problem. -A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 9 m down from the top of the dome the ceiling is 8 m wide, Find the best location for the light source.

Solve the problem. -A projectile is thrown upward so that its distance above the ground after ttt seconds is h=−14t2+560th = - 14 t ^ { 2 } + 560 \mathrm { t }h=−14t2+560t . After how many seconds does it reach its maximum height?

Find the eccentricity of the ellipse. - x2+25y2=25x ^ { 2 } + 25 y ^ { 2 } = 25x2+25y2=25

Graph the ellipse. - 4(x−2)2+9(y+1)2=364(x-2)^{2}+9(y+1)^{2}=364(x−2)2+9(y+1)2=36

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Further Topics in Algebra

Review of Basic Concepts

Filters

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the sum of the distances from the points $( 2,0 )$ and $( - 2,0 )$ is 21 .

Write an equation for the ellipse. -foci at $( \pm 6,0 ) ; x$ -intercepts $\pm 10$

Write an equation for the parabola with vertex at the origin. -Focus $( 0 , - 3 )$

Write an equation for the parabola. -vertex $( - 6 , - 7 )$ , focus $( - 6 , - 11 )$

Write an equation for the ellipse. -eccentricity $\frac { 3 } { 5 }$ ; vertices at $( 0 , - 5 ) , ( 0,5 )$

Write an equation for the parabola with vertex at the origin. -Through $( 3 , - 3 \sqrt { 3 } )$ , symmetric with respect to the $x$ -axis

Write an equation for the parabola. -vertex $( 3 , - 7 )$ , focus $( 3 , - 2 )$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $4 x ^ { 2 } = 16 - 4 y ^ { 2 }$

Write an equation for the hyperbola. -foci at $( 6 - 2 \sqrt { 29 } , 9 ) , ( 6 + 2 \sqrt { 29 } , 9 )$ ; eccentricity $\frac { 2 \sqrt { 29 } } { 10 }$

Write the word or phrase that best completes each statement or answers the question. - $36 \mathrm { y } ^ { 2 } = 576 - 4 \mathrm { x } ^ { 2 }$

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x = 8 y ^ { 2 } - 5 y + 7$

Write an equation for the parabola with vertex at the origin. -Through $( - 2,2 )$ , opening to the left

Write an equation for the hyperbola. -center at $( 1 , - 8 ) ;$ focus at $( 1 - 2 \sqrt { 17 } , - 8 ) ;$ eccentricity $\frac { 2 \sqrt { 17 } } { 8 }$

Solve the problem. -A projectile is thrown upward so that its distance above the ground after $t$ seconds is $h = - 14 t ^ { 2 } + 560 \mathrm { t }$ . After how many seconds does it reach its maximum height?

Find the eccentricity of the ellipse. - $x ^ { 2 } + 25 y ^ { 2 } = 25$

Graph the ellipse. - $4(x-2)^{2}+9(y+1)^{2}=36$ $Graph the ellipse. - 4(x-2)^{2}+9(y+1)^{2}=36$