Exam 11: Analytic Geometry

Provide an appropriate response. - $\frac { x ^ { 2 } } { 100 } - \frac { y ^ { 2 } } { 16 } = 1 \text { and } \frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 100 } = 1$ are identical. Is the student correct? Explain.

(Essay)

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Question 181

Graph the conic section. - $x ^ { 2 } - 9 y - 6 x = 0$ $Graph the conic section. - x ^ { 2 } - 9 y - 6 x = 0$

(Multiple Choice)

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Question 182

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $x ^ { 2 } - y ^ { 2 } = 25$

(Multiple Choice)

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Question 183

Provide an appropriate response. -Explain why the vertex of a parabola must lie on its axis.

(Essay)

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Question 184

Provide an appropriate response. -Fill in the blanks to complete the statement. The graph of $\mathrm { P } ( \mathrm { x } ) = 6 ( \mathrm { x } - 4 ) ^ { 2 } - 7$ is a parabola with axis of symmetry........ and vertex...........

(Multiple Choice)

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Question 185

Identify the type of graph. - $\frac { x ^ { 2 } } { 12 } = 1 - \frac { y ^ { 2 } } { 3 }$

(Multiple Choice)

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Question 186

Write an equation for the parabola with vertex at the origin. -Through $( 2,2 )$ , symmetric with respect to the y-axis

(Multiple Choice)

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Question 187

Write an equation for the hyperbola. -The roof of a building is in the shape of the hyperbola $3 y ^ { 2 } - x ^ { 2 } = 28$ , where $x$ and $y$ are in meters. Refer to the figure and determine the height, $h$ , of the outside walls. $A = 9 \mathrm {~m}$ $Write an equation for the hyperbola. -The roof of a building is in the shape of the hyperbola 3 y ^ { 2 } - x ^ { 2 } = 28 , where x and y are in meters. Refer to the figure and determine the height, h , of the outside walls. A = 9 \mathrm {~m}$

(Multiple Choice)

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Question 188

Graph the hyperbola. - $\frac { ( x + 2 ) ^ { 2 } } { 9 } - \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$ $Graph the hyperbola. - \frac { ( x + 2 ) ^ { 2 } } { 9 } - \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$

(Multiple Choice)

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Question 189

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

(Multiple Choice)

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Question 190

Match the equation of the parabola with the appropriate description. - $y = - 3 x ^ { 2 } + 6 x + 3$

(Multiple Choice)

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Question 191

Write an equation for the parabola. -vertex $( 6 , - 7 )$ , focus $( 9 , - 7 )$

(Multiple Choice)

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Question 192

Write an equation for the parabola. -vertex $( 9 , - 10 )$ , focus $( 9 , - 6 )$

(Multiple Choice)

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Question 193

Provide an appropriate response. -Explain in your own words how you can tell from the equation whether the graph is a 216) circle or an ellipse.

(Essay)

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Question 194

Provide an appropriate response. -A parabola has eccentricity between 0 and 1.

(True/False)

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Question 195

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { ( x - 2 ) ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$

(Multiple Choice)

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Question 196

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $( x - 5 ) ^ { 2 } = 36 - y ^ { 2 }$

(Multiple Choice)

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Question 197

Write an equation for the parabola. -vertex: $( - 2,5 )$ , directrix: $y = 10$

(Multiple Choice)

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Question 198

Write an equation for the parabola with vertex at the origin. -Through $( 7,6 )$ , opening to the right

(Multiple Choice)

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Question 199

Find the eccentricity of the conic section shown in the graph. - $y = - 17$

(Multiple Choice)

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Question 200

Showing 181 - 200 of 217

Provide an appropriate response. - $\frac { x ^ { 2 } } { 100 } - \frac { y ^ { 2 } } { 16 } = 1 \text { and } \frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 100 } = 1$ are identical. Is the student correct? Explain.

Graph the conic section. - $x ^ { 2 } - 9 y - 6 x = 0$ $Graph the conic section. - x ^ { 2 } - 9 y - 6 x = 0$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $x ^ { 2 } - y ^ { 2 } = 25$

Provide an appropriate response. -Explain why the vertex of a parabola must lie on its axis.

Provide an appropriate response. -Fill in the blanks to complete the statement. The graph of $\mathrm { P } ( \mathrm { x } ) = 6 ( \mathrm { x } - 4 ) ^ { 2 } - 7$ is a parabola with axis of symmetry........ and vertex...........

Identify the type of graph. - $\frac { x ^ { 2 } } { 12 } = 1 - \frac { y ^ { 2 } } { 3 }$

Write an equation for the parabola with vertex at the origin. -Through $( 2,2 )$ , symmetric with respect to the y-axis

Graph the hyperbola. - $\frac { ( x + 2 ) ^ { 2 } } { 9 } - \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$ $Graph the hyperbola. - \frac { ( x + 2 ) ^ { 2 } } { 9 } - \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$

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

Match the equation of the parabola with the appropriate description. - $y = - 3 x ^ { 2 } + 6 x + 3$

Write an equation for the parabola. -vertex $( 6 , - 7 )$ , focus $( 9 , - 7 )$

Write an equation for the parabola. -vertex $( 9 , - 10 )$ , focus $( 9 , - 6 )$

Provide an appropriate response. -Explain in your own words how you can tell from the equation whether the graph is a 216) circle or an ellipse.

Provide an appropriate response. -A parabola has eccentricity between 0 and 1.

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { ( x - 2 ) ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $( x - 5 ) ^ { 2 } = 36 - y ^ { 2 }$

Write an equation for the parabola. -vertex: $( - 2,5 )$ , directrix: $y = 10$

Write an equation for the parabola with vertex at the origin. -Through $( 7,6 )$ , opening to the right

Find the eccentricity of the conic section shown in the graph. - $y = - 17$

Review of Basic Concepts

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

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Exam 11: Analytic Geometry

Provide an appropriate response. - x2100−y216=1 and y216−x2100=1\frac { x ^ { 2 } } { 100 } - \frac { y ^ { 2 } } { 16 } = 1 \text { and } \frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 100 } = 1100x2​−16y2​=1 and 16y2​−100x2​=1 are identical. Is the student correct? Explain.

Graph the conic section. - x2−9y−6x=0x ^ { 2 } - 9 y - 6 x = 0x2−9y−6x=0

Identify the equation as a parabola, circle, ellipse, or hyperbola. - x2−y2=25x ^ { 2 } - y ^ { 2 } = 25x2−y2=25

Provide an appropriate response. -Explain why the vertex of a parabola must lie on its axis.

Provide an appropriate response. -Fill in the blanks to complete the statement. The graph of P(x)=6(x−4)2−7\mathrm { P } ( \mathrm { x } ) = 6 ( \mathrm { x } - 4 ) ^ { 2 } - 7P(x)=6(x−4)2−7 is a parabola with axis of symmetry........ and vertex...........

Identify the type of graph. - x212=1−y23\frac { x ^ { 2 } } { 12 } = 1 - \frac { y ^ { 2 } } { 3 }12x2​=1−3y2​

Write an equation for the parabola with vertex at the origin. -Through (2,2)( 2,2 )(2,2) , symmetric with respect to the y-axis

Write an equation for the hyperbola. -The roof of a building is in the shape of the hyperbola 3y2−x2=283 y ^ { 2 } - x ^ { 2 } = 283y2−x2=28 , where xxx and yyy are in meters. Refer to the figure and determine the height, hhh , of the outside walls. A=9 mA = 9 \mathrm {~m}A=9 m

Graph the hyperbola. - (x+2)29−(y−1)225=1\frac { ( x + 2 ) ^ { 2 } } { 9 } - \frac { ( y - 1 ) ^ { 2 } } { 25 } = 19(x+2)2​−25(y−1)2​=1

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

Match the equation of the parabola with the appropriate description. - y=−3x2+6x+3y = - 3 x ^ { 2 } + 6 x + 3y=−3x2+6x+3

Write an equation for the parabola. -vertex (6,−7)( 6 , - 7 )(6,−7) , focus (9,−7)( 9 , - 7 )(9,−7)

Write an equation for the parabola. -vertex (9,−10)( 9 , - 10 )(9,−10) , focus (9,−6)( 9 , - 6 )(9,−6)

Provide an appropriate response. -Explain in your own words how you can tell from the equation whether the graph is a 216) circle or an ellipse.

Provide an appropriate response. -A parabola has eccentricity between 0 and 1.

Determine the two equations necessary to graph the ellipse with a graphing calculator. - (x−2)264+y225=1\frac { ( x - 2 ) ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 164(x−2)2​+25y2​=1

Identify the equation as a parabola, circle, ellipse, or hyperbola. - (x−5)2=36−y2( x - 5 ) ^ { 2 } = 36 - y ^ { 2 }(x−5)2=36−y2

Write an equation for the parabola. -vertex: (−2,5)( - 2,5 )(−2,5) , directrix: y=10y = 10y=10

Write an equation for the parabola with vertex at the origin. -Through (7,6)( 7,6 )(7,6) , opening to the right

Find the eccentricity of the conic section shown in the graph. - y=−17y = - 17y=−17

Review of Basic Concepts

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

Filters

Provide an appropriate response. - $\frac { x ^ { 2 } } { 100 } - \frac { y ^ { 2 } } { 16 } = 1 \text { and } \frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 100 } = 1$ are identical. Is the student correct? Explain.

Graph the conic section. - $x ^ { 2 } - 9 y - 6 x = 0$ $Graph the conic section. - x ^ { 2 } - 9 y - 6 x = 0$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $x ^ { 2 } - y ^ { 2 } = 25$

Provide an appropriate response. -Fill in the blanks to complete the statement. The graph of $\mathrm { P } ( \mathrm { x } ) = 6 ( \mathrm { x } - 4 ) ^ { 2 } - 7$ is a parabola with axis of symmetry........ and vertex...........

Identify the type of graph. - $\frac { x ^ { 2 } } { 12 } = 1 - \frac { y ^ { 2 } } { 3 }$

Write an equation for the parabola with vertex at the origin. -Through $( 2,2 )$ , symmetric with respect to the y-axis

Graph the hyperbola. - $\frac { ( x + 2 ) ^ { 2 } } { 9 } - \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$ $Graph the hyperbola. - \frac { ( x + 2 ) ^ { 2 } } { 9 } - \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$

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

Match the equation of the parabola with the appropriate description. - $y = - 3 x ^ { 2 } + 6 x + 3$

Write an equation for the parabola. -vertex $( 6 , - 7 )$ , focus $( 9 , - 7 )$

Write an equation for the parabola. -vertex $( 9 , - 10 )$ , focus $( 9 , - 6 )$

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { ( x - 2 ) ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $( x - 5 ) ^ { 2 } = 36 - y ^ { 2 }$

Write an equation for the parabola. -vertex: $( - 2,5 )$ , directrix: $y = 10$

Write an equation for the parabola with vertex at the origin. -Through $( 7,6 )$ , opening to the right

Find the eccentricity of the conic section shown in the graph. - $y = - 17$