Exam 9: Analytic Geometry

Graph the curve whose parametric equations are given. - $x=t^{3}+1, y=t^{3}-10 ;-2 \leq t \leq 2$ $Graph the curve whose parametric equations are given. - x=t^{3}+1, y=t^{3}-10 ;-2 \leq t \leq 2$

(Multiple Choice)

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Question 141

Find an equation for the parabola described. -Vertex at $( 3 , - 4 )$ ; focus at $( 3 , - 6 )$

(Multiple Choice)

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Question 142

Convert the polar equation to a rectangular equation. - $r = \frac { 4 } { 4 + \cos \theta }$

(Multiple Choice)

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Question 143

Solve the problem. -An arch for a bridge over a highway is in the form of a semiellipse. The top of the arch is 35 feet above ground (the major axis). What should the span of the bridge be (the length of its minor axis) if the height 30 feet from the Center is to be 10 feet above ground?

(Multiple Choice)

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Question 144

Find an equation for the ellipse described. -Center $( 0,0 )$ ; major axis horizontal with length 10 ; length of minor axis is 4

(Multiple Choice)

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Question 145

Solve the problem. -An arch in the form of a semiellipse is 52 ft wide at the base and has a height of 20 ft. How wide is the arch at a height of 12 ft above the base?

(Multiple Choice)

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Question 146

Find the center, foci, and vertices of the ellipse. - $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 1$

(Multiple Choice)

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Question 147

Solve the problem. -A searchlight is shaped like a paraboloid of revolution. If the light source is located 5 feet from the base along the axis of symmetry and the opening is 8 feet across, how deep should the searchlight be?

(Multiple Choice)

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Question 148

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - $x y+16=0$ \ $Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - x y+16=0 \$

(Multiple Choice)

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Question 149

Identify the equation without completing the square. - $2 x ^ { 2 } + 4 y ^ { 2 } - 3 x - 1 = 0$

(Multiple Choice)

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Question 150

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $( x - 3 ) ^ { 2 } - 9 ( y + 3 ) ^ { 2 } = 9$

(Multiple Choice)

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Question 151

Find parametric equations for the rectangular equation. - $y = x ^ { 4 } - 4$

(Multiple Choice)

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Question 152

Solve the problem. -A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex to the focus is 31 feet and the distance across the top of the mirror is 66 inches, how deep is the mirror in the center?

(Multiple Choice)

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Question 153

Find the vertex, focus, and directrix of the parabola with the given equation. - $( y + 1 ) ^ { 2 } = 16 ( x + 3 )$

(Multiple Choice)

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Question 154

Find a polar equation for the conic. A focus is at the pole. - $e = \frac { 1 } { 2 } ;$ directrix is perpendicular to the polar axis 2 to the left of the pole

(Multiple Choice)

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Question 155

Find an equation of the parabola described. -Focus at (5, 0); vertex at (0, 0)

(Multiple Choice)

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Question 156

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

(Multiple Choice)

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Question 157

Choose the one alternative that best completes the statement or answers the question. -A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? Round answer to two decimal places.

(Multiple Choice)

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(80)

Question 158

Match the equation to its graph. - $y ^ { 2 } = - 10 x$

(Multiple Choice)

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Question 159

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

(Multiple Choice)

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Question 160

Showing 141 - 160 of 200

Graph the curve whose parametric equations are given. - $x=t^{3}+1, y=t^{3}-10 ;-2 \leq t \leq 2$ $Graph the curve whose parametric equations are given. - x=t^{3}+1, y=t^{3}-10 ;-2 \leq t \leq 2$

Find an equation for the parabola described. -Vertex at $( 3 , - 4 )$ ; focus at $( 3 , - 6 )$

Convert the polar equation to a rectangular equation. - $r = \frac { 4 } { 4 + \cos \theta }$

Solve the problem. -An arch for a bridge over a highway is in the form of a semiellipse. The top of the arch is 35 feet above ground (the major axis). What should the span of the bridge be (the length of its minor axis) if the height 30 feet from the Center is to be 10 feet above ground?

Find an equation for the ellipse described. -Center $( 0,0 )$ ; major axis horizontal with length 10 ; length of minor axis is 4

Solve the problem. -An arch in the form of a semiellipse is 52 ft wide at the base and has a height of 20 ft. How wide is the arch at a height of 12 ft above the base?

Find the center, foci, and vertices of the ellipse. - $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 1$

Solve the problem. -A searchlight is shaped like a paraboloid of revolution. If the light source is located 5 feet from the base along the axis of symmetry and the opening is 8 feet across, how deep should the searchlight be?

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - $x y+16=0$ \ $Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - x y+16=0 \$

Identify the equation without completing the square. - $2 x ^ { 2 } + 4 y ^ { 2 } - 3 x - 1 = 0$

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $( x - 3 ) ^ { 2 } - 9 ( y + 3 ) ^ { 2 } = 9$

Find parametric equations for the rectangular equation. - $y = x ^ { 4 } - 4$

Solve the problem. -A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex to the focus is 31 feet and the distance across the top of the mirror is 66 inches, how deep is the mirror in the center?

Find the vertex, focus, and directrix of the parabola with the given equation. - $( y + 1 ) ^ { 2 } = 16 ( x + 3 )$

Find a polar equation for the conic. A focus is at the pole. - $e = \frac { 1 } { 2 } ;$ directrix is perpendicular to the polar axis 2 to the left of the pole

Find an equation of the parabola described. -Focus at (5, 0); vertex at (0, 0)

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

Choose the one alternative that best completes the statement or answers the question. -A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? Round answer to two decimal places.

Match the equation to its graph. - $y ^ { 2 } = - 10 x$

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

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

Graph the curve whose parametric equations are given. - x=t3+1,y=t3−10;−2≤t≤2x=t^{3}+1, y=t^{3}-10 ;-2 \leq t \leq 2x=t3+1,y=t3−10;−2≤t≤2

Find an equation for the parabola described. -Vertex at (3,−4)( 3 , - 4 )(3,−4) ; focus at (3,−6)( 3 , - 6 )(3,−6)

Convert the polar equation to a rectangular equation. - r=44+cos⁡θr = \frac { 4 } { 4 + \cos \theta }r=4+cosθ4​

Solve the problem. -An arch for a bridge over a highway is in the form of a semiellipse. The top of the arch is 35 feet above ground (the major axis). What should the span of the bridge be (the length of its minor axis) if the height 30 feet from the Center is to be 10 feet above ground?

Find an equation for the ellipse described. -Center (0,0)( 0,0 )(0,0) ; major axis horizontal with length 10 ; length of minor axis is 4

Solve the problem. -An arch in the form of a semiellipse is 52 ft wide at the base and has a height of 20 ft. How wide is the arch at a height of 12 ft above the base?

Find the center, foci, and vertices of the ellipse. - x281+y29=1\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 181x2​+9y2​=1

Solve the problem. -A searchlight is shaped like a paraboloid of revolution. If the light source is located 5 feet from the base along the axis of symmetry and the opening is 8 feet across, how deep should the searchlight be?

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - xy+16=0x y+16=0xy+16=0 \

Identify the equation without completing the square. - 2x2+4y2−3x−1=02 x ^ { 2 } + 4 y ^ { 2 } - 3 x - 1 = 02x2+4y2−3x−1=0

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - (x−3)2−9(y+3)2=9( x - 3 ) ^ { 2 } - 9 ( y + 3 ) ^ { 2 } = 9(x−3)2−9(y+3)2=9

Find parametric equations for the rectangular equation. - y=x4−4y = x ^ { 4 } - 4y=x4−4

Solve the problem. -A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex to the focus is 31 feet and the distance across the top of the mirror is 66 inches, how deep is the mirror in the center?

Find the vertex, focus, and directrix of the parabola with the given equation. - (y+1)2=16(x+3)( y + 1 ) ^ { 2 } = 16 ( x + 3 )(y+1)2=16(x+3)

Find a polar equation for the conic. A focus is at the pole. - e=12;e = \frac { 1 } { 2 } ;e=21​; directrix is perpendicular to the polar axis 2 to the left of the pole

Find an equation of the parabola described. -Focus at (5, 0); vertex at (0, 0)

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

Choose the one alternative that best completes the statement or answers the question. -A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? Round answer to two decimal places.

Match the equation to its graph. - y2=−10xy ^ { 2 } = - 10 xy2=−10x

Graph the equation. - 9(x+2)2+4(y−1)2=369(x+2)^{2}+4(y-1)^{2}=369(x+2)2+4(y−1)2=36

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

Graph the curve whose parametric equations are given. - $x=t^{3}+1, y=t^{3}-10 ;-2 \leq t \leq 2$ $Graph the curve whose parametric equations are given. - x=t^{3}+1, y=t^{3}-10 ;-2 \leq t \leq 2$

Find an equation for the parabola described. -Vertex at $( 3 , - 4 )$ ; focus at $( 3 , - 6 )$

Convert the polar equation to a rectangular equation. - $r = \frac { 4 } { 4 + \cos \theta }$

Find an equation for the ellipse described. -Center $( 0,0 )$ ; major axis horizontal with length 10 ; length of minor axis is 4

Find the center, foci, and vertices of the ellipse. - $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 1$

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - $x y+16=0$ \ $Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - x y+16=0 \$

Identify the equation without completing the square. - $2 x ^ { 2 } + 4 y ^ { 2 } - 3 x - 1 = 0$

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $( x - 3 ) ^ { 2 } - 9 ( y + 3 ) ^ { 2 } = 9$

Find parametric equations for the rectangular equation. - $y = x ^ { 4 } - 4$

Find the vertex, focus, and directrix of the parabola with the given equation. - $( y + 1 ) ^ { 2 } = 16 ( x + 3 )$

Find a polar equation for the conic. A focus is at the pole. - $e = \frac { 1 } { 2 } ;$ directrix is perpendicular to the polar axis 2 to the left of the pole

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

Match the equation to its graph. - $y ^ { 2 } = - 10 x$

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