Exam 9: Analytic Geometry

Choose the one alternative that best completes the statement or answers the question. Match the equation to the graph. - $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 4 } = 1$

(Multiple Choice)

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Question 181

Find an equation for the ellipse described. -Center at $( 0,0 )$ ; focus at $( - 5,0 )$ ; vertex at $( 8,0 )$

(Multiple Choice)

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Question 182

Identify the conic that the polar equation represents. Also, give the position of the directrix. - $r = \frac { 5 } { 6 - 3 \sin \theta }$

(Multiple Choice)

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Question 183

Find an equation for the ellipse described. Graph the equation. -Foci at $( - 4 , - 1 )$ and $( 2 , - 1 )$ ; length of major axis is 10

(Multiple Choice)

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Question 184

Match the graph to its equation. -

(Multiple Choice)

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Question 185

Write the word or phrase that best completes each statement or answers the question. -A race track is in the shape of an ellipse 80 feet long and 60 feet wide. What is the width 32 feet from the center?

(Short Answer)

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Question 186

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1$

(Multiple Choice)

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Question 187

Find an equation for the ellipse described. -Center at $( 0,0 )$ ; focus at $( 0,5 )$ ; vertex at $( 0 , - 7 )$

(Multiple Choice)

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Question 188

Write an equation for the hyperbola. -

(Multiple Choice)

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Question 189

Graph the curve whose parametric equations are given. - $x = - \sec t , y = \tan t ; - \frac { \pi } { 2 } < t < \frac { \pi } { 2 }$ $Graph the curve whose parametric equations are given. - x = - \sec t , y = \tan t ; - \frac { \pi } { 2 } < t < \frac { \pi } { 2 }$

(Multiple Choice)

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Question 190

Write an equation for the parabola. -

(Multiple Choice)

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Question 191

Solve the problem. -The roof of a building is in the shape of the hyperbola $\mathrm { y } ^ { 2 } - \mathrm { x } ^ { 2 } = 33$ , where $\mathrm { x }$ and $\mathrm { y }$ are in meters. Refer to the figure and determine the height $h$ of the outside walls. $Solve the problem. -The roof of a building is in the shape of the hyperbola \mathrm { y } ^ { 2 } - \mathrm { x } ^ { 2 } = 33 , where \mathrm { x } and \mathrm { y } are in meters. Refer to the figure and determine the height h of the outside walls. a = b = 7 m$ $a = b = 7 m$

(Multiple Choice)

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Question 192

Match the equation to the graph. - $( x + 2 ) ^ { 2 } = - 6 ( y + 2 )$

(Multiple Choice)

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Question 193

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - $24 x y-7 y^{2}+36=0$ $Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - 24 x y-7 y^{2}+36=0$

(Multiple Choice)

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Question 194

Find the asymptotes of the hyperbola. - $x ^ { 2 } - y ^ { 2 } - 6 x + 8 y - 11 = 0$

(Multiple Choice)

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Question 195

Match the graph to its equation. -

(Multiple Choice)

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Question 196

Identify the conic that the polar equation represents. Also, give the position of the directrix. - $r = \frac { 2 } { 1 - 2 \cos \theta }$

(Multiple Choice)

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Question 197

Graph the equation. - $(x+1)^{2}=-8(y-2)$ $Graph the equation. - (x+1)^{2}=-8(y-2)$

(Multiple Choice)

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Question 198

Find an equation for the ellipse described. Graph the equation. -Foci at $( - 1,4 )$ and $( - 5,4 )$ ; vertex at $( - 7,4 )$

(Multiple Choice)

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Question 199

Find an equation for the ellipse described. -Center at $( 0,0 )$ ; focus at $( 0,2 )$ ; vertex at $( 0,3 )$

(Multiple Choice)

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Question 200

Showing 181 - 200 of 200

Choose the one alternative that best completes the statement or answers the question. Match the equation to the graph. - $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 4 } = 1$

Find an equation for the ellipse described. -Center at $( 0,0 )$ ; focus at $( - 5,0 )$ ; vertex at $( 8,0 )$

Identify the conic that the polar equation represents. Also, give the position of the directrix. - $r = \frac { 5 } { 6 - 3 \sin \theta }$

Find an equation for the ellipse described. Graph the equation. -Foci at $( - 4 , - 1 )$ and $( 2 , - 1 )$ ; length of major axis is 10

Match the graph to its equation. -

Write the word or phrase that best completes each statement or answers the question. -A race track is in the shape of an ellipse 80 feet long and 60 feet wide. What is the width 32 feet from the center?

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1$

Find an equation for the ellipse described. -Center at $( 0,0 )$ ; focus at $( 0,5 )$ ; vertex at $( 0 , - 7 )$

Write an equation for the hyperbola. -

Graph the curve whose parametric equations are given. - $x = - \sec t , y = \tan t ; - \frac { \pi } { 2 } < t < \frac { \pi } { 2 }$ $Graph the curve whose parametric equations are given. - x = - \sec t , y = \tan t ; - \frac { \pi } { 2 } < t < \frac { \pi } { 2 }$

Write an equation for the parabola. -

Match the equation to the graph. - $( x + 2 ) ^ { 2 } = - 6 ( y + 2 )$

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - $24 x y-7 y^{2}+36=0$ $Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - 24 x y-7 y^{2}+36=0$

Find the asymptotes of the hyperbola. - $x ^ { 2 } - y ^ { 2 } - 6 x + 8 y - 11 = 0$

Match the graph to its equation. -

Identify the conic that the polar equation represents. Also, give the position of the directrix. - $r = \frac { 2 } { 1 - 2 \cos \theta }$

Graph the equation. - $(x+1)^{2}=-8(y-2)$ $Graph the equation. - (x+1)^{2}=-8(y-2)$

Find an equation for the ellipse described. Graph the equation. -Foci at $( - 1,4 )$ and $( - 5,4 )$ ; vertex at $( - 7,4 )$

Find an equation for the ellipse described. -Center at $( 0,0 )$ ; focus at $( 0,2 )$ ; vertex at $( 0,3 )$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 9: Analytic Geometry

Choose the one alternative that best completes the statement or answers the question. Match the equation to the graph. - y216−x24=1\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 4 } = 116y2​−4x2​=1

Find an equation for the ellipse described. -Center at (0,0)( 0,0 )(0,0) ; focus at (−5,0)( - 5,0 )(−5,0) ; vertex at (8,0)( 8,0 )(8,0)

Identify the conic that the polar equation represents. Also, give the position of the directrix. - r=56−3sin⁡θr = \frac { 5 } { 6 - 3 \sin \theta }r=6−3sinθ5​

Find an equation for the ellipse described. Graph the equation. -Foci at (−4,−1)( - 4 , - 1 )(−4,−1) and (2,−1)( 2 , - 1 )(2,−1) ; length of major axis is 10

Match the graph to its equation. -

Write the word or phrase that best completes each statement or answers the question. -A race track is in the shape of an ellipse 80 feet long and 60 feet wide. What is the width 32 feet from the center?

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - x236−y24=1\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 136x2​−4y2​=1

Find an equation for the ellipse described. -Center at (0,0)( 0,0 )(0,0) ; focus at (0,5)( 0,5 )(0,5) ; vertex at (0,−7)( 0 , - 7 )(0,−7)

Write an equation for the hyperbola. -

Graph the curve whose parametric equations are given. - x=−sec⁡t,y=tan⁡t;−π2<t<π2x = - \sec t , y = \tan t ; - \frac { \pi } { 2 } < t < \frac { \pi } { 2 }x=−sect,y=tant;−2π​<t<2π​

Write an equation for the parabola. -

Match the equation to the graph. - (x+2)2=−6(y+2)( x + 2 ) ^ { 2 } = - 6 ( y + 2 )(x+2)2=−6(y+2)

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - 24xy−7y2+36=024 x y-7 y^{2}+36=024xy−7y2+36=0

Find the asymptotes of the hyperbola. - x2−y2−6x+8y−11=0x ^ { 2 } - y ^ { 2 } - 6 x + 8 y - 11 = 0x2−y2−6x+8y−11=0

Match the graph to its equation. -

Identify the conic that the polar equation represents. Also, give the position of the directrix. - r=21−2cos⁡θr = \frac { 2 } { 1 - 2 \cos \theta }r=1−2cosθ2​

Graph the equation. - (x+1)2=−8(y−2)(x+1)^{2}=-8(y-2)(x+1)2=−8(y−2)

Find an equation for the ellipse described. Graph the equation. -Foci at (−1,4)( - 1,4 )(−1,4) and (−5,4)( - 5,4 )(−5,4) ; vertex at (−7,4)( - 7,4 )(−7,4)

Find an equation for the ellipse described. -Center at (0,0)( 0,0 )(0,0) ; focus at (0,2)( 0,2 )(0,2) ; vertex at (0,3)( 0,3 )(0,3)

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Choose the one alternative that best completes the statement or answers the question. Match the equation to the graph. - $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 4 } = 1$

Find an equation for the ellipse described. -Center at $( 0,0 )$ ; focus at $( - 5,0 )$ ; vertex at $( 8,0 )$

Identify the conic that the polar equation represents. Also, give the position of the directrix. - $r = \frac { 5 } { 6 - 3 \sin \theta }$

Find an equation for the ellipse described. Graph the equation. -Foci at $( - 4 , - 1 )$ and $( 2 , - 1 )$ ; length of major axis is 10

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1$

Find an equation for the ellipse described. -Center at $( 0,0 )$ ; focus at $( 0,5 )$ ; vertex at $( 0 , - 7 )$

Graph the curve whose parametric equations are given. - $x = - \sec t , y = \tan t ; - \frac { \pi } { 2 } < t < \frac { \pi } { 2 }$ $Graph the curve whose parametric equations are given. - x = - \sec t , y = \tan t ; - \frac { \pi } { 2 } < t < \frac { \pi } { 2 }$

Match the equation to the graph. - $( x + 2 ) ^ { 2 } = - 6 ( y + 2 )$

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - $24 x y-7 y^{2}+36=0$ $Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - 24 x y-7 y^{2}+36=0$

Find the asymptotes of the hyperbola. - $x ^ { 2 } - y ^ { 2 } - 6 x + 8 y - 11 = 0$

Identify the conic that the polar equation represents. Also, give the position of the directrix. - $r = \frac { 2 } { 1 - 2 \cos \theta }$

Graph the equation. - $(x+1)^{2}=-8(y-2)$ $Graph the equation. - (x+1)^{2}=-8(y-2)$

Find an equation for the ellipse described. Graph the equation. -Foci at $( - 1,4 )$ and $( - 5,4 )$ ; vertex at $( - 7,4 )$

Find an equation for the ellipse described. -Center at $( 0,0 )$ ; focus at $( 0,2 )$ ; vertex at $( 0,3 )$