Exam 10: Conic Sections and Analytic Geometry

Solve Applied Problems Involving Hyperbolas -Two LORAN stations are positioned 208 miles apart along a straight shore. A ship records a time difference of $0.00097$ seconds between the LORAN signals. (The radio signals travel at 186,000 miles per second.) Where will the ship reach shore if it were to follow the hyperbola corresponding to this time difference? If the ship is 150 miles offshore, what is the position of the ship?

(Multiple Choice)

4.7/5

(37)

Question 61

Additional Concepts - $\left\{\begin{array}{l}x^{2}+y^{2}=25 \\25 x^{2}+9 y^{2}=225\end{array}\right.$ $Additional Concepts - \left\{\begin{array}{l} x^{2}+y^{2}=25 \\ 25 x^{2}+9 y^{2}=225 \end{array}\right.$

(Multiple Choice)

4.9/5

(42)

Question 62

Tech: Rotation of Axes - $16 x^{2}-24 x y+9 y^{2}-3 x-4 y=0$ $Tech: Rotation of Axes - 16 x^{2}-24 x y+9 y^{2}-3 x-4 y=0$

(Multiple Choice)

4.9/5

(34)

Question 63

Write Equations of Parabolas in Standard Form -Focus: $( 2,5 )$ ; Directrix: $y = - 3$

(Multiple Choice)

4.7/5

(28)

Question 64

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

(Multiple Choice)

4.9/5

(32)

Question 65

The Parabola 1 Graph Parabolas with Vertices at the Origin - $x ^ { 2 } = 8 y$

(Multiple Choice)

4.9/5

(37)

Question 66

Convert the equation to the standard form for a hyperbola by completing the square on x and y. - $9 x ^ { 2 } - 4 y ^ { 2 } + 18 x - 16 y - 43 = 0$

(Multiple Choice)

4.8/5

(33)

Question 67

Additional Concepts - $5 x ^ { 2 } + 4 \sqrt { 3 } x y + y ^ { 2 } - 35 = 0$ ; Find the equations of the asymptotes.

(Multiple Choice)

4.9/5

(32)

Question 68

Convert the equation to the standard form for a hyperbola by completing the square on x and y. - $y ^ { 2 } - 4 x ^ { 2 } - 4 y - 16 x - 16 = 0$

(Multiple Choice)

4.9/5

(36)

Question 69

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

(Multiple Choice)

4.8/5

(30)

Question 70

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

(Multiple Choice)

4.8/5

(32)

Question 71

Graph the ellipse and locate the foci. - $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 1$ $Graph the ellipse and locate the foci. - \frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 1$

(Multiple Choice)

4.9/5

(32)

Question 72

Rotation of Axes 1 Identify Conics Without Completing the Square - $3 x ^ { 2 } - 4 x + y - 3 = 0$

(Multiple Choice)

4.8/5

(29)

Question 73

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

(Multiple Choice)

4.8/5

(28)

Question 74

Eliminate the Parameter - $x = 6 \sin t , y = 6 \cos t ; 0 \leq t \leq 2 \pi$

(Multiple Choice)

4.8/5

(29)

Question 75

Graph the ellipse and locate the foci. - $16 x^{2}+9 y^{2}=144$ $Graph the ellipse and locate the foci. - 16 x^{2}+9 y^{2}=144$

(Multiple Choice)

4.7/5

(40)

Question 76

Rotation of Axes 1 Identify Conics Without Completing the Square - $2 x ^ { 2 } + 4 y ^ { 2 } - 4 x - 1 = 0$

(Multiple Choice)

4.8/5

(28)

Question 77

Additional Concepts - $y ^ { 2 } - 6 y - x + 3 = 0$

(Multiple Choice)

4.8/5

(34)

Question 78

Eliminate the Parameter -An ellipse: $x = 5 + 2 \cos t , y = 1 + 3 \sin t$

(Multiple Choice)

4.7/5

(31)

Question 79

Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. - -=196 +=196 $Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. - \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 196 \\ x ^ { 2 } + y ^ { 2 } = 196 \end{array}$

(Multiple Choice)

4.8/5

(36)

Question 80

Showing 61 - 80 of 228

Additional Concepts - $\left\{\begin{array}{l}x^{2}+y^{2}=25 \\25 x^{2}+9 y^{2}=225\end{array}\right.$ $Additional Concepts - \left\{\begin{array}{l} x^{2}+y^{2}=25 \\ 25 x^{2}+9 y^{2}=225 \end{array}\right.$

Tech: Rotation of Axes - $16 x^{2}-24 x y+9 y^{2}-3 x-4 y=0$ $Tech: Rotation of Axes - 16 x^{2}-24 x y+9 y^{2}-3 x-4 y=0$

Write Equations of Parabolas in Standard Form -Focus: $( 2,5 )$ ; Directrix: $y = - 3$

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

The Parabola 1 Graph Parabolas with Vertices at the Origin - $x ^ { 2 } = 8 y$

Convert the equation to the standard form for a hyperbola by completing the square on x and y. - $9 x ^ { 2 } - 4 y ^ { 2 } + 18 x - 16 y - 43 = 0$

Additional Concepts - $5 x ^ { 2 } + 4 \sqrt { 3 } x y + y ^ { 2 } - 35 = 0$ ; Find the equations of the asymptotes.

Convert the equation to the standard form for a hyperbola by completing the square on x and y. - $y ^ { 2 } - 4 x ^ { 2 } - 4 y - 16 x - 16 = 0$

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

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

Graph the ellipse and locate the foci. - $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 1$ $Graph the ellipse and locate the foci. - \frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 1$

Rotation of Axes 1 Identify Conics Without Completing the Square - $3 x ^ { 2 } - 4 x + y - 3 = 0$

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

Eliminate the Parameter - $x = 6 \sin t , y = 6 \cos t ; 0 \leq t \leq 2 \pi$

Graph the ellipse and locate the foci. - $16 x^{2}+9 y^{2}=144$ $Graph the ellipse and locate the foci. - 16 x^{2}+9 y^{2}=144$

Rotation of Axes 1 Identify Conics Without Completing the Square - $2 x ^ { 2 } + 4 y ^ { 2 } - 4 x - 1 = 0$

Additional Concepts - $y ^ { 2 } - 6 y - x + 3 = 0$

Eliminate the Parameter -An ellipse: $x = 5 + 2 \cos t , y = 1 + 3 \sin t$

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

Additional Concepts - {x2+y2=2525x2+9y2=225\left\{\begin{array}{l}x^{2}+y^{2}=25 \\25 x^{2}+9 y^{2}=225\end{array}\right.{x2+y2=2525x2+9y2=225​

Tech: Rotation of Axes - 16x2−24xy+9y2−3x−4y=016 x^{2}-24 x y+9 y^{2}-3 x-4 y=016x2−24xy+9y2−3x−4y=0

Write Equations of Parabolas in Standard Form -Focus: (2,5)( 2,5 )(2,5) ; Directrix: y=−3y = - 3y=−3

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

The Parabola 1 Graph Parabolas with Vertices at the Origin - x2=8yx ^ { 2 } = 8 yx2=8y

Convert the equation to the standard form for a hyperbola by completing the square on x and y. - 9x2−4y2+18x−16y−43=09 x ^ { 2 } - 4 y ^ { 2 } + 18 x - 16 y - 43 = 09x2−4y2+18x−16y−43=0

Additional Concepts - 5x2+43xy+y2−35=05 x ^ { 2 } + 4 \sqrt { 3 } x y + y ^ { 2 } - 35 = 05x2+43​xy+y2−35=0 ; Find the equations of the asymptotes.

Convert the equation to the standard form for a hyperbola by completing the square on x and y. - y2−4x2−4y−16x−16=0y ^ { 2 } - 4 x ^ { 2 } - 4 y - 16 x - 16 = 0y2−4x2−4y−16x−16=0

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

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

Graph the ellipse and locate the foci. - x29+y25=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 19x2​+5y2​=1

Rotation of Axes 1 Identify Conics Without Completing the Square - 3x2−4x+y−3=03 x ^ { 2 } - 4 x + y - 3 = 03x2−4x+y−3=0

Graph Ellipses Not Centered at the Origin - 9(x−1)2+16(y+2)2=1449(x-1)^{2}+16(y+2)^{2}=1449(x−1)2+16(y+2)2=144

Eliminate the Parameter - x=6sin⁡t,y=6cos⁡t;0≤t≤2πx = 6 \sin t , y = 6 \cos t ; 0 \leq t \leq 2 \pix=6sint,y=6cost;0≤t≤2π

Graph the ellipse and locate the foci. - 16x2+9y2=14416 x^{2}+9 y^{2}=14416x2+9y2=144

Rotation of Axes 1 Identify Conics Without Completing the Square - 2x2+4y2−4x−1=02 x ^ { 2 } + 4 y ^ { 2 } - 4 x - 1 = 02x2+4y2−4x−1=0

Additional Concepts - y2−6y−x+3=0y ^ { 2 } - 6 y - x + 3 = 0y2−6y−x+3=0

Eliminate the Parameter -An ellipse: x=5+2cos⁡t,y=1+3sin⁡tx = 5 + 2 \cos t , y = 1 + 3 \sin tx=5+2cost,y=1+3sint

Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. - -=196 +=196

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 - $\left\{\begin{array}{l}x^{2}+y^{2}=25 \\25 x^{2}+9 y^{2}=225\end{array}\right.$ $Additional Concepts - \left\{\begin{array}{l} x^{2}+y^{2}=25 \\ 25 x^{2}+9 y^{2}=225 \end{array}\right.$

Tech: Rotation of Axes - $16 x^{2}-24 x y+9 y^{2}-3 x-4 y=0$ $Tech: Rotation of Axes - 16 x^{2}-24 x y+9 y^{2}-3 x-4 y=0$

Write Equations of Parabolas in Standard Form -Focus: $( 2,5 )$ ; Directrix: $y = - 3$

The Parabola 1 Graph Parabolas with Vertices at the Origin - $x ^ { 2 } = 8 y$

Convert the equation to the standard form for a hyperbola by completing the square on x and y. - $9 x ^ { 2 } - 4 y ^ { 2 } + 18 x - 16 y - 43 = 0$

Additional Concepts - $5 x ^ { 2 } + 4 \sqrt { 3 } x y + y ^ { 2 } - 35 = 0$ ; Find the equations of the asymptotes.

Convert the equation to the standard form for a hyperbola by completing the square on x and y. - $y ^ { 2 } - 4 x ^ { 2 } - 4 y - 16 x - 16 = 0$

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

Graph the ellipse and locate the foci. - $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 1$ $Graph the ellipse and locate the foci. - \frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 1$

Rotation of Axes 1 Identify Conics Without Completing the Square - $3 x ^ { 2 } - 4 x + y - 3 = 0$

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

Eliminate the Parameter - $x = 6 \sin t , y = 6 \cos t ; 0 \leq t \leq 2 \pi$

Graph the ellipse and locate the foci. - $16 x^{2}+9 y^{2}=144$ $Graph the ellipse and locate the foci. - 16 x^{2}+9 y^{2}=144$

Rotation of Axes 1 Identify Conics Without Completing the Square - $2 x ^ { 2 } + 4 y ^ { 2 } - 4 x - 1 = 0$

Additional Concepts - $y ^ { 2 } - 6 y - x + 3 = 0$

Eliminate the Parameter -An ellipse: $x = 5 + 2 \cos t , y = 1 + 3 \sin t$