Exam 10: Conic Sections and Analytic Geometry

Solve Applied Problems Involving Parabolas -A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 32 feet. If the distance across the top of the mirror is 78 inches, how deep is the mirror in the center?

(Multiple Choice)

4.7/5

(30)

Question 161

Sketch the function represented by the given parametric equations. Then use the graph to determine each of the following: a. intervals, if any, on which the function is increasing and intervals, if any, on which the function is decreasing. b. the number, if any, at which the function has a maximum and this maximum value, or the number, if any, at which the function has a minimum and this minimum value. - $x = 2 ^ { t } , y = t$ $Sketch the function represented by the given parametric equations. Then use the graph to determine each of the following: a. intervals, if any, on which the function is increasing and intervals, if any, on which the function is decreasing. b. the number, if any, at which the function has a maximum and this maximum value, or the number, if any, at which the function has a minimum and this minimum value. - x = 2 ^ { t } , y = t$

(Multiple Choice)

4.8/5

(32)

Question 162

Additional Concepts - $x = - ( y + 8 ) ^ { 2 } + 1$

(Multiple Choice)

4.9/5

(37)

Question 163

Conic Sections in Polar Coordinates 1 Define Conics in Terms of a Focus and a Directrix - $r = \frac { 5 } { 4 + 2 \cos \theta }$

(Multiple Choice)

4.8/5

(31)

Question 164

Use the center, vertices, and asymptotes to graph the hyperbola. - $(y-2)^{2}-(x+1)^{2}=5$ $Use the center, vertices, and asymptotes to graph the hyperbola. - (y-2)^{2}-(x+1)^{2}=5$

(Multiple Choice)

4.7/5

(38)

Question 165

Graph the parabola. - $y ^ { 2 } + 16 x = 0$ $Graph the parabola. - y ^ { 2 } + 16 x = 0$

(Multiple Choice)

4.9/5

(31)

Question 166

Graph Ellipses Not Centered at the Origin - $25 ( x + 2 ) ^ { 2 } + 36 ( y - 3 ) ^ { 2 } = 900$

(Multiple Choice)

4.9/5

(34)

Question 167

Rotation of Axes 1 Identify Conics Without Completing the Square - $2 x ^ { 2 } - 3 y ^ { 2 } + 5 x + 2 y + 3 = 0$

(Multiple Choice)

4.8/5

(28)

Question 168

Write Equations of Hyperbolas in Standard Form -Foci: $( - 9,0 ) , ( 9,0 )$ ; vertices: $( - 5,0 ) , ( 5,0 )$

(Multiple Choice)

4.7/5

(30)

Question 169

Find the standard form of the equation of the hyperbola. -

(Multiple Choice)

4.9/5

(34)

Question 170

Write Equations of Parabolas in Standard Form -Focus: $( 0,8 )$ ; Directrix: $y = - 8$

(Multiple Choice)

4.9/5

(33)

Question 171

Use point plotting to graph the plane curve described by the given parametric equations. - $x=t^{2}, y=\sqrt{t}+2 ; 0 \leq t \leq 4$ $Use point plotting to graph the plane curve described by the given parametric equations. - x=t^{2}, y=\sqrt{t}+2 ; 0 \leq t \leq 4$

(Multiple Choice)

4.8/5

(46)

Question 172

Solve Applied Problems Involving Parabolas -An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 6.25 inches tall and stand 50 inches apart. Find the vertical distance from the roadway to the cable at a point on the road 7.5 inches from the lowest point of the cable.

(Multiple Choice)

4.8/5

(26)

Question 173

Solve Applied Problems Involving Ellipses -The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the ar

(Multiple Choice)

4.8/5

(33)

Question 174

Graph Ellipses Not Centered at the Origin - $16(x+2)^{2}+9(y-1)^{2}=144$ $Graph Ellipses Not Centered at the Origin - 16(x+2)^{2}+9(y-1)^{2}=144$

(Multiple Choice)

4.9/5

(39)

Question 175

Find the standard form of the equation of the hyperbola. -

(Multiple Choice)

4.8/5

(32)

Question 176

Tech: Rotation of Axes - $2 x^{2}+4 \sqrt{3 x y}+6 y^{2}+\sqrt{3 x}-y=0$ $Tech: Rotation of Axes - 2 x^{2}+4 \sqrt{3 x y}+6 y^{2}+\sqrt{3 x}-y=0$

(Multiple Choice)

4.9/5

(33)

Question 177

Write Equations of Hyperbolas in Standard Form -Endpoints of transverse axis: $( 0 , - 6 ) , ( 0,6 )$ ; asymptote: $y = \frac { 3 } { 10 } x$

(Multiple Choice)

4.9/5

(43)

Question 178

Write Equations of Rotated Conics in Standard Form - $24 x y - 7 y ^ { 2 } + 36 = 0$

(Multiple Choice)

4.8/5

(34)

Question 179

Write Equations of Ellipses in Standard Form - Center at $( - 1,2 )$

(Multiple Choice)

4.9/5

(40)

Question 180

Showing 161 - 180 of 228

Solve Applied Problems Involving Parabolas -A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 32 feet. If the distance across the top of the mirror is 78 inches, how deep is the mirror in the center?

Additional Concepts - $x = - ( y + 8 ) ^ { 2 } + 1$

Conic Sections in Polar Coordinates 1 Define Conics in Terms of a Focus and a Directrix - $r = \frac { 5 } { 4 + 2 \cos \theta }$

Use the center, vertices, and asymptotes to graph the hyperbola. - $(y-2)^{2}-(x+1)^{2}=5$ $Use the center, vertices, and asymptotes to graph the hyperbola. - (y-2)^{2}-(x+1)^{2}=5$

Graph the parabola. - $y ^ { 2 } + 16 x = 0$ $Graph the parabola. - y ^ { 2 } + 16 x = 0$

Graph Ellipses Not Centered at the Origin - $25 ( x + 2 ) ^ { 2 } + 36 ( y - 3 ) ^ { 2 } = 900$

Rotation of Axes 1 Identify Conics Without Completing the Square - $2 x ^ { 2 } - 3 y ^ { 2 } + 5 x + 2 y + 3 = 0$

Write Equations of Hyperbolas in Standard Form -Foci: $( - 9,0 ) , ( 9,0 )$ ; vertices: $( - 5,0 ) , ( 5,0 )$

Find the standard form of the equation of the hyperbola. -

Write Equations of Parabolas in Standard Form -Focus: $( 0,8 )$ ; Directrix: $y = - 8$

Use point plotting to graph the plane curve described by the given parametric equations. - $x=t^{2}, y=\sqrt{t}+2 ; 0 \leq t \leq 4$ $Use point plotting to graph the plane curve described by the given parametric equations. - x=t^{2}, y=\sqrt{t}+2 ; 0 \leq t \leq 4$

Solve Applied Problems Involving Ellipses -The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the ar

Graph Ellipses Not Centered at the Origin - $16(x+2)^{2}+9(y-1)^{2}=144$ $Graph Ellipses Not Centered at the Origin - 16(x+2)^{2}+9(y-1)^{2}=144$

Find the standard form of the equation of the hyperbola. -

Tech: Rotation of Axes - $2 x^{2}+4 \sqrt{3 x y}+6 y^{2}+\sqrt{3 x}-y=0$ $Tech: Rotation of Axes - 2 x^{2}+4 \sqrt{3 x y}+6 y^{2}+\sqrt{3 x}-y=0$

Write Equations of Hyperbolas in Standard Form -Endpoints of transverse axis: $( 0 , - 6 ) , ( 0,6 )$ ; asymptote: $y = \frac { 3 } { 10 } x$

Write Equations of Rotated Conics in Standard Form - $24 x y - 7 y ^ { 2 } + 36 = 0$

Write Equations of Ellipses in Standard Form - Center at $( - 1,2 )$

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 10: Conic Sections and Analytic Geometry

Solve Applied Problems Involving Parabolas -A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 32 feet. If the distance across the top of the mirror is 78 inches, how deep is the mirror in the center?

Additional Concepts - x=−(y+8)2+1x = - ( y + 8 ) ^ { 2 } + 1x=−(y+8)2+1

Conic Sections in Polar Coordinates 1 Define Conics in Terms of a Focus and a Directrix - r=54+2cos⁡θr = \frac { 5 } { 4 + 2 \cos \theta }r=4+2cosθ5​

Use the center, vertices, and asymptotes to graph the hyperbola. - (y−2)2−(x+1)2=5(y-2)^{2}-(x+1)^{2}=5(y−2)2−(x+1)2=5

Graph the parabola. - y2+16x=0y ^ { 2 } + 16 x = 0y2+16x=0

Graph Ellipses Not Centered at the Origin - 25(x+2)2+36(y−3)2=90025 ( x + 2 ) ^ { 2 } + 36 ( y - 3 ) ^ { 2 } = 90025(x+2)2+36(y−3)2=900

Rotation of Axes 1 Identify Conics Without Completing the Square - 2x2−3y2+5x+2y+3=02 x ^ { 2 } - 3 y ^ { 2 } + 5 x + 2 y + 3 = 02x2−3y2+5x+2y+3=0

Write Equations of Hyperbolas in Standard Form -Foci: (−9,0),(9,0)( - 9,0 ) , ( 9,0 )(−9,0),(9,0) ; vertices: (−5,0),(5,0)( - 5,0 ) , ( 5,0 )(−5,0),(5,0)

Find the standard form of the equation of the hyperbola. -

Write Equations of Parabolas in Standard Form -Focus: (0,8)( 0,8 )(0,8) ; Directrix: y=−8y = - 8y=−8

Use point plotting to graph the plane curve described by the given parametric equations. - x=t2,y=t+2;0≤t≤4x=t^{2}, y=\sqrt{t}+2 ; 0 \leq t \leq 4x=t2,y=t​+2;0≤t≤4

Solve Applied Problems Involving Ellipses -The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the ar

Graph Ellipses Not Centered at the Origin - 16(x+2)2+9(y−1)2=14416(x+2)^{2}+9(y-1)^{2}=14416(x+2)2+9(y−1)2=144

Find the standard form of the equation of the hyperbola. -

Tech: Rotation of Axes - 2x2+43xy+6y2+3x−y=02 x^{2}+4 \sqrt{3 x y}+6 y^{2}+\sqrt{3 x}-y=02x2+43xy​+6y2+3x​−y=0

Write Equations of Hyperbolas in Standard Form -Endpoints of transverse axis: (0,−6),(0,6)( 0 , - 6 ) , ( 0,6 )(0,−6),(0,6) ; asymptote: y=310xy = \frac { 3 } { 10 } xy=103​x

Write Equations of Rotated Conics in Standard Form - 24xy−7y2+36=024 x y - 7 y ^ { 2 } + 36 = 024xy−7y2+36=0

Write Equations of Ellipses in Standard Form - Center at (−1,2)( - 1,2 )(−1,2)

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Additional Concepts - $x = - ( y + 8 ) ^ { 2 } + 1$

Conic Sections in Polar Coordinates 1 Define Conics in Terms of a Focus and a Directrix - $r = \frac { 5 } { 4 + 2 \cos \theta }$

Use the center, vertices, and asymptotes to graph the hyperbola. - $(y-2)^{2}-(x+1)^{2}=5$ $Use the center, vertices, and asymptotes to graph the hyperbola. - (y-2)^{2}-(x+1)^{2}=5$

Graph the parabola. - $y ^ { 2 } + 16 x = 0$ $Graph the parabola. - y ^ { 2 } + 16 x = 0$

Graph Ellipses Not Centered at the Origin - $25 ( x + 2 ) ^ { 2 } + 36 ( y - 3 ) ^ { 2 } = 900$

Rotation of Axes 1 Identify Conics Without Completing the Square - $2 x ^ { 2 } - 3 y ^ { 2 } + 5 x + 2 y + 3 = 0$

Write Equations of Hyperbolas in Standard Form -Foci: $( - 9,0 ) , ( 9,0 )$ ; vertices: $( - 5,0 ) , ( 5,0 )$

Write Equations of Parabolas in Standard Form -Focus: $( 0,8 )$ ; Directrix: $y = - 8$

Use point plotting to graph the plane curve described by the given parametric equations. - $x=t^{2}, y=\sqrt{t}+2 ; 0 \leq t \leq 4$ $Use point plotting to graph the plane curve described by the given parametric equations. - x=t^{2}, y=\sqrt{t}+2 ; 0 \leq t \leq 4$

Graph Ellipses Not Centered at the Origin - $16(x+2)^{2}+9(y-1)^{2}=144$ $Graph Ellipses Not Centered at the Origin - 16(x+2)^{2}+9(y-1)^{2}=144$

Tech: Rotation of Axes - $2 x^{2}+4 \sqrt{3 x y}+6 y^{2}+\sqrt{3 x}-y=0$ $Tech: Rotation of Axes - 2 x^{2}+4 \sqrt{3 x y}+6 y^{2}+\sqrt{3 x}-y=0$

Write Equations of Hyperbolas in Standard Form -Endpoints of transverse axis: $( 0 , - 6 ) , ( 0,6 )$ ; asymptote: $y = \frac { 3 } { 10 } x$

Write Equations of Rotated Conics in Standard Form - $24 x y - 7 y ^ { 2 } + 36 = 0$

Write Equations of Ellipses in Standard Form - Center at $( - 1,2 )$