Exam 8: Analytic Geometry in Two and Three Dimensions

Find an equation in standard form for the ellipse that satisfies the given conditions. -An ellipse with foci at $( - 1,3 )$ and $( 5,3 )$ ; major axis length of 10

(Multiple Choice)

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Question 121

Solve the problem. -Find the vector equation of the line through $A$ and $B$ . $A = ( 7,6 , - 7 ) , B = ( 1 , - 3 , - 9 ) , C = ( 6 , - 8,7 )$

(Multiple Choice)

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Question 122

Graph the parabola. - $y = \frac { 2 } { 3 } ( x - 2 ) ^ { 2 } + 4$ $Graph the parabola. - y = \frac { 2 } { 3 } ( x - 2 ) ^ { 2 } + 4$

(Multiple Choice)

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Question 123

Graph the hyperbola. - $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 64 } = 1$ $Graph the hyperbola. - \frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 64 } = 1$

(Multiple Choice)

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Question 124

Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. - $10 y ^ { 2 } + 9 x + 10 y + 10 = 0$

(Multiple Choice)

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Question 125

Convert the equation to Cartesian form. - $r = \frac { 8 } { 5 - 4 \cos \theta }$

(Multiple Choice)

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Question 126

Find parametric equations for the line described below. -The line through the points $P ( - 1 , - 1 , - 4 )$ and $Q ( 4,6,4 )$

(Multiple Choice)

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Question 127

Find the center, vertices, and foci of the ellipse with the given equation. - $\frac { ( x - 4 ) ^ { 2 } } { 64 } + \frac { ( y - 2 ) ^ { 2 } } { 100 } = 1$

(Multiple Choice)

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Question 128

Find an equation in standard form for the ellipse that satisfies the given conditions. -Major axis endpoints $( 0 , \pm 9 )$ , minor axis length 10

(Multiple Choice)

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Question 129

Graph the hyperbola. - $\frac { ( x + 2 ) ^ { 2 } } { 64 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$ $Graph the hyperbola. - \frac { ( x + 2 ) ^ { 2 } } { 64 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$

(Multiple Choice)

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Question 130

Find an equation in standard form for the ellipse that satisfies the given conditions. -An ellipse with intercepts $( \pm 5,0 )$ and $( 0 , \pm 6 )$ , center at origin

(Multiple Choice)

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Question 131

Find an equation that matches the parabola's graph. -

(Multiple Choice)

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Question 132

Solve the problem. -The roof of a building is in the shape of the hyperbola $y ^ { 2 } - x ^ { 2 } = 66$ , where $x$ and $y$ are in meters. Determine the distance, w, the outside walls are apart, if the height of each wall is $10 \mathrm {~m}$ . $Solve the problem. -The roof of a building is in the shape of the hyperbola y ^ { 2 } - x ^ { 2 } = 66 , where x and y are in meters. Determine the distance, w, the outside walls are apart, if the height of each wall is 10 \mathrm {~m} .$

(Multiple Choice)

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Question 133

Graph the hyperbola. - $\frac { ( y + 2 ) ^ { 2 } } { 64 } - \frac { ( x + 1 ) ^ { 2 } } { 9 } = 1$ $Graph the hyperbola. - \frac { ( y + 2 ) ^ { 2 } } { 64 } - \frac { ( x + 1 ) ^ { 2 } } { 9 } = 1$

(Multiple Choice)

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Question 134

Match the given graph with its equation. -

(Multiple Choice)

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Question 135

Graph the ellipse. - $9(x+4)^{2}+4(y+6)^{2}=36$ $Graph the ellipse. - 9(x+4)^{2}+4(y+6)^{2}=36$

(Multiple Choice)

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Question 136

Match the given graph with its equation. -

(Multiple Choice)

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Question 137

Match the given graph with its equation. -

(Multiple Choice)

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Question 138

Find the standard form of the equation of the parabola. -Focus at $( 10,5 )$ , directrix $x = 8$

(Multiple Choice)

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Question 139

Find the standard form of the equation of the parabola. -Vertex at the origin, focus at $( 0,4 )$

(Multiple Choice)

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Question 140

Showing 121 - 140 of 167

Find an equation in standard form for the ellipse that satisfies the given conditions. -An ellipse with foci at $( - 1,3 )$ and $( 5,3 )$ ; major axis length of 10

Solve the problem. -Find the vector equation of the line through $A$ and $B$ . $A = ( 7,6 , - 7 ) , B = ( 1 , - 3 , - 9 ) , C = ( 6 , - 8,7 )$

Graph the parabola. - $y = \frac { 2 } { 3 } ( x - 2 ) ^ { 2 } + 4$ $Graph the parabola. - y = \frac { 2 } { 3 } ( x - 2 ) ^ { 2 } + 4$

Graph the hyperbola. - $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 64 } = 1$ $Graph the hyperbola. - \frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 64 } = 1$

Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. - $10 y ^ { 2 } + 9 x + 10 y + 10 = 0$

Convert the equation to Cartesian form. - $r = \frac { 8 } { 5 - 4 \cos \theta }$

Find parametric equations for the line described below. -The line through the points $P ( - 1 , - 1 , - 4 )$ and $Q ( 4,6,4 )$

Find the center, vertices, and foci of the ellipse with the given equation. - $\frac { ( x - 4 ) ^ { 2 } } { 64 } + \frac { ( y - 2 ) ^ { 2 } } { 100 } = 1$

Find an equation in standard form for the ellipse that satisfies the given conditions. -Major axis endpoints $( 0 , \pm 9 )$ , minor axis length 10

Graph the hyperbola. - $\frac { ( x + 2 ) ^ { 2 } } { 64 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$ $Graph the hyperbola. - \frac { ( x + 2 ) ^ { 2 } } { 64 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$

Find an equation in standard form for the ellipse that satisfies the given conditions. -An ellipse with intercepts $( \pm 5,0 )$ and $( 0 , \pm 6 )$ , center at origin

Find an equation that matches the parabola's graph. -

Graph the hyperbola. - $\frac { ( y + 2 ) ^ { 2 } } { 64 } - \frac { ( x + 1 ) ^ { 2 } } { 9 } = 1$ $Graph the hyperbola. - \frac { ( y + 2 ) ^ { 2 } } { 64 } - \frac { ( x + 1 ) ^ { 2 } } { 9 } = 1$

Match the given graph with its equation. -

Graph the ellipse. - $9(x+4)^{2}+4(y+6)^{2}=36$ $Graph the ellipse. - 9(x+4)^{2}+4(y+6)^{2}=36$

Match the given graph with its equation. -

Match the given graph with its equation. -

Find the standard form of the equation of the parabola. -Focus at $( 10,5 )$ , directrix $x = 8$

Find the standard form of the equation of the parabola. -Vertex at the origin, focus at $( 0,4 )$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

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Exam 8: Analytic Geometry in Two and Three Dimensions

Find an equation in standard form for the ellipse that satisfies the given conditions. -An ellipse with foci at (−1,3)( - 1,3 )(−1,3) and (5,3)( 5,3 )(5,3) ; major axis length of 10

Solve the problem. -Find the vector equation of the line through AAA and BBB . A=(7,6,−7),B=(1,−3,−9),C=(6,−8,7)A = ( 7,6 , - 7 ) , B = ( 1 , - 3 , - 9 ) , C = ( 6 , - 8,7 )A=(7,6,−7),B=(1,−3,−9),C=(6,−8,7)

Graph the parabola. - y=23(x−2)2+4y = \frac { 2 } { 3 } ( x - 2 ) ^ { 2 } + 4y=32​(x−2)2+4

Graph the hyperbola. - y225−x264=1\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 64 } = 125y2​−64x2​=1

Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. - 10y2+9x+10y+10=010 y ^ { 2 } + 9 x + 10 y + 10 = 010y2+9x+10y+10=0

Convert the equation to Cartesian form. - r=85−4cos⁡θr = \frac { 8 } { 5 - 4 \cos \theta }r=5−4cosθ8​

Find parametric equations for the line described below. -The line through the points P(−1,−1,−4)P ( - 1 , - 1 , - 4 )P(−1,−1,−4) and Q(4,6,4)Q ( 4,6,4 )Q(4,6,4)

Find the center, vertices, and foci of the ellipse with the given equation. - (x−4)264+(y−2)2100=1\frac { ( x - 4 ) ^ { 2 } } { 64 } + \frac { ( y - 2 ) ^ { 2 } } { 100 } = 164(x−4)2​+100(y−2)2​=1

Find an equation in standard form for the ellipse that satisfies the given conditions. -Major axis endpoints (0,±9)( 0 , \pm 9 )(0,±9) , minor axis length 10

Graph the hyperbola. - (x+2)264−(y−2)236=1\frac { ( x + 2 ) ^ { 2 } } { 64 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 164(x+2)2​−36(y−2)2​=1

Find an equation in standard form for the ellipse that satisfies the given conditions. -An ellipse with intercepts (±5,0)( \pm 5,0 )(±5,0) and (0,±6)( 0 , \pm 6 )(0,±6) , center at origin

Find an equation that matches the parabola's graph. -

Solve the problem. -The roof of a building is in the shape of the hyperbola y2−x2=66y ^ { 2 } - x ^ { 2 } = 66y2−x2=66 , where xxx and yyy are in meters. Determine the distance, w, the outside walls are apart, if the height of each wall is 10 m10 \mathrm {~m}10 m .

Graph the hyperbola. - (y+2)264−(x+1)29=1\frac { ( y + 2 ) ^ { 2 } } { 64 } - \frac { ( x + 1 ) ^ { 2 } } { 9 } = 164(y+2)2​−9(x+1)2​=1

Match the given graph with its equation. -

Graph the ellipse. - 9(x+4)2+4(y+6)2=369(x+4)^{2}+4(y+6)^{2}=369(x+4)2+4(y+6)2=36

Match the given graph with its equation. -

Match the given graph with its equation. -

Find the standard form of the equation of the parabola. -Focus at (10,5)( 10,5 )(10,5) , directrix x=8x = 8x=8

Find the standard form of the equation of the parabola. -Vertex at the origin, focus at (0,4)( 0,4 )(0,4)

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Find an equation in standard form for the ellipse that satisfies the given conditions. -An ellipse with foci at $( - 1,3 )$ and $( 5,3 )$ ; major axis length of 10

Solve the problem. -Find the vector equation of the line through $A$ and $B$ . $A = ( 7,6 , - 7 ) , B = ( 1 , - 3 , - 9 ) , C = ( 6 , - 8,7 )$

Graph the parabola. - $y = \frac { 2 } { 3 } ( x - 2 ) ^ { 2 } + 4$ $Graph the parabola. - y = \frac { 2 } { 3 } ( x - 2 ) ^ { 2 } + 4$

Graph the hyperbola. - $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 64 } = 1$ $Graph the hyperbola. - \frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 64 } = 1$

Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. - $10 y ^ { 2 } + 9 x + 10 y + 10 = 0$

Convert the equation to Cartesian form. - $r = \frac { 8 } { 5 - 4 \cos \theta }$

Find parametric equations for the line described below. -The line through the points $P ( - 1 , - 1 , - 4 )$ and $Q ( 4,6,4 )$

Find the center, vertices, and foci of the ellipse with the given equation. - $\frac { ( x - 4 ) ^ { 2 } } { 64 } + \frac { ( y - 2 ) ^ { 2 } } { 100 } = 1$

Find an equation in standard form for the ellipse that satisfies the given conditions. -Major axis endpoints $( 0 , \pm 9 )$ , minor axis length 10

Graph the hyperbola. - $\frac { ( x + 2 ) ^ { 2 } } { 64 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$ $Graph the hyperbola. - \frac { ( x + 2 ) ^ { 2 } } { 64 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$

Find an equation in standard form for the ellipse that satisfies the given conditions. -An ellipse with intercepts $( \pm 5,0 )$ and $( 0 , \pm 6 )$ , center at origin

Graph the hyperbola. - $\frac { ( y + 2 ) ^ { 2 } } { 64 } - \frac { ( x + 1 ) ^ { 2 } } { 9 } = 1$ $Graph the hyperbola. - \frac { ( y + 2 ) ^ { 2 } } { 64 } - \frac { ( x + 1 ) ^ { 2 } } { 9 } = 1$

Graph the ellipse. - $9(x+4)^{2}+4(y+6)^{2}=36$ $Graph the ellipse. - 9(x+4)^{2}+4(y+6)^{2}=36$

Find the standard form of the equation of the parabola. -Focus at $( 10,5 )$ , directrix $x = 8$

Find the standard form of the equation of the parabola. -Vertex at the origin, focus at $( 0,4 )$