Question 1

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

Accepted Answer

A)  ellipse 
B)  parabola 
C)  circle 
D)  hyperbola 
A)  ellipse 
B)  parabola 
C)  circle 
D)  hyperbola

Question 2

Convert the equation to the standard form for an ellipse by completing the square on x and y.
-$$4 x ^ { 2 } + 16 y ^ { 2 } + 8 x + 96 y + 84 = 0$$

Accepted Answer

A)  $\frac { ( x + 1 ) ^ { 2 } } { 16 } + \frac { ( y + 3 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( x + 3 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x - 1 ) ^ { 2 } } { 16 } + \frac { ( y - 3 ) ^ { 2 } } { 4 } = 1$ 
A)  $\frac { ( x + 1 ) ^ { 2 } } { 16 } + \frac { ( y + 3 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( x + 3 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x - 1 ) ^ { 2 } } { 16 } + \frac { ( y - 3 ) ^ { 2 } } { 4 } = 1$

Question 3

Use point plotting to graph the plane curve described by the given parametric equations.
-$x=5 \sin t, y=5 \cos t ; 0 \leq t \leq 2 \pi$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 4

Graph Hyperbolas Centered at the Origin
-$16 x^{2}-9 y^{2}=144$

Accepted Answer

A)  Asymptotes: $\mathrm { y } = \pm \frac { 4 } { 3 } \mathrm { x }$
  
B)  Asymptotes: $y = \pm \frac { 3 } { 4 } x$
  
C)  Asymptotes: $y = \pm \frac { 3 } { 4 } x$
  
D)  Asymptotes: $\mathrm { y } = \pm \frac { 4 } { 3 } \mathrm { x }$
  
A)  Asymptotes: $\mathrm { y } = \pm \frac { 4 } { 3 } \mathrm { x }$
  
B)  Asymptotes: $y = \pm \frac { 3 } { 4 } x$
  
C)  Asymptotes: $y = \pm \frac { 3 } { 4 } x$
  
D)  Asymptotes: $\mathrm { y } = \pm \frac { 4 } { 3 } \mathrm { x }$

Question 5

Find the standard form of the equation of the ellipse satisfying the given conditions.
-Endpoints of major axis: $( 1 , - 3 )$ and $( 1,7 )$; endpoints of minor axis: $( - 3,2 )$ and $( 5,2 )$;

Accepted Answer

A)  $\frac { ( x - 1 ) ^ { 2 } } { 16 } + \frac { ( y - 2 ) ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { 16 } + \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$ 
A)  $\frac { ( x - 1 ) ^ { 2 } } { 16 } + \frac { ( y - 2 ) ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { 16 } + \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$

Question 6

Graph Ellipses Not Centered at the Origin
-$$\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 7

Tech: Rotation of Axes
-

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 8

Use the rotated system to graph the equation.
-$3 x^{2}-2 \sqrt{3} x y+y^{2}-8 x-8 \sqrt{3} y=0$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 9

Eliminate the Parameter
-$x = \sqrt { t } , y = 2 t + 4 ; 0 \leq t \leq 4$

Accepted Answer

A)  $y = 2 x ^ { 2 } + 4 ; 0 \leq x \leq 2$ 
B)  $y = 4 x ^ { 2 } + 2 ; - 1 \leq x \leq 2$ 
C)  $y = - 4 x ^ { 2 } + 17 ; 0 \leq x \leq 2$ 
D)  $\mathrm { y } = - 4 \mathrm { x } + 17 ; 0 \leq \mathrm { x } \leq 2$ 
A)  $y = 2 x ^ { 2 } + 4 ; 0 \leq x \leq 2$ 
B)  $y = 4 x ^ { 2 } + 2 ; - 1 \leq x \leq 2$ 
C)  $y = - 4 x ^ { 2 } + 17 ; 0 \leq x \leq 2$ 
D)  $\mathrm { y } = - 4 \mathrm { x } + 17 ; 0 \leq \mathrm { x } \leq 2$

Question 10

Match the equation to the graph.
-$$y ^ { 2 } = - 4 x$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 11

The Parabola
1 Graph Parabolas with Vertices at the Origin
-$$y ^ { 2 } = 12 x$$

Accepted Answer

A)  focus: $( 3,0 )$
directrix: $x = - 3$ 
B)  focus: $( 0,3 )$
directrix: $y = - 3$ 
C)  focus: $( 3,0 )$
directrix: $x = 3$ 
D)  focus: $( 0 , - 3 )$
directrix: $y = - 3$ 
A)  focus: $( 3,0 )$
directrix: $x = - 3$ 
B)  focus: $( 0,3 )$
directrix: $y = - 3$ 
C)  focus: $( 3,0 )$
directrix: $x = 3$ 
D)  focus: $( 0 , - 3 )$
directrix: $y = - 3$

Question 12

Write Equations of Hyperbolas in Standard Form
-Endpoints of transverse axis: $( - 5,0 ) , ( 5,0 )$; foci: $( - 11,0 ) , ( - 11,0 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 96 } = 1$ 
B)  $\frac { x ^ { 2 } } { 96 } - \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 121 } = 1$ 
D)  $\frac { x ^ { 2 } } { 121 } - \frac { y ^ { 2 } } { 25 } = 1$ 
A)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 96 } = 1$ 
B)  $\frac { x ^ { 2 } } { 96 } - \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 121 } = 1$ 
D)  $\frac { x ^ { 2 } } { 121 } - \frac { y ^ { 2 } } { 25 } = 1$

Question 13

Use point plotting to graph the plane curve described by the given parametric equations.
-$x=2 t, y=|t-1| ;-\infty \leq t \leq \infty$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 14

Find a set of parametric equations for the rectangular equation.
-$y = x ^ { 4 } - 3$

Accepted Answer

A)  $x = t ; y = t ^ { 4 } - 3$ 
B)  $x = t ^ { 2 } ; y = t ^ { 2 } - 3$ 
C)  $x = t ^ { 2 } ; y = t ^ { 4 } - 3$ 
D)  $x = t ; y = t ^ { 2 } - 3$ 
A)  $x = t ; y = t ^ { 4 } - 3$ 
B)  $x = t ^ { 2 } ; y = t ^ { 2 } - 3$ 
C)  $x = t ^ { 2 } ; y = t ^ { 4 } - 3$ 
D)  $x = t ; y = t ^ { 2 } - 3$

Question 15

Write the appropriate rotation formulas so that in a rotated system the equation has no x'y'-term.
-$$6 x ^ { 2 } - 4 x y + 3 y ^ { 2 } - 8 x + 8 y = 0$$

Accepted Answer

A)  $x = \sqrt { 5 } \left( \frac { x ^ { \prime } - 2 y ^ { \prime } } { 5 } \right) ; y = \sqrt { 5 } \left( \frac { 2 x ^ { \prime } + y ^ { \prime } } { 5 } \right)$ 
B)  $x = \sqrt { 5 } \left( \frac { 2 x ^ { \prime } - y ^ { \prime } } { 5 } \right) ; y = \sqrt { 5 } \left( \frac { x ^ { \prime } + 2 y ^ { \prime } } { 5 } \right)$ 
C)  $x = \frac { 3 } { 5 } x ^ { \prime } - \frac { 4 } { 5 } y ^ { \prime } ; y = \frac { 4 } { 5 } x ^ { \prime } + \frac { 3 } { 5 } y ^ { \prime }$ 
D)  $x = \frac { 7 } { 25 } x ^ { \prime } - \frac { 24 } { 25 } y ^ { \prime } ; y = \frac { 24 } { 25 } x ^ { \prime } + \frac { 7 } { 25 } y ^ { \prime }$ 
A)  $x = \sqrt { 5 } \left( \frac { x ^ { \prime } - 2 y ^ { \prime } } { 5 } \right) ; y = \sqrt { 5 } \left( \frac { 2 x ^ { \prime } + y ^ { \prime } } { 5 } \right)$ 
B)  $x = \sqrt { 5 } \left( \frac { 2 x ^ { \prime } - y ^ { \prime } } { 5 } \right) ; y = \sqrt { 5 } \left( \frac { x ^ { \prime } + 2 y ^ { \prime } } { 5 } \right)$ 
C)  $x = \frac { 3 } { 5 } x ^ { \prime } - \frac { 4 } { 5 } y ^ { \prime } ; y = \frac { 4 } { 5 } x ^ { \prime } + \frac { 3 } { 5 } y ^ { \prime }$ 
D)  $x = \frac { 7 } { 25 } x ^ { \prime } - \frac { 24 } { 25 } y ^ { \prime } ; y = \frac { 24 } { 25 } x ^ { \prime } + \frac { 7 } { 25 } y ^ { \prime }$

Question 16

Tech: Rotation of Axes
-$5 x^{2}+3 x y+5 y^{2}=11$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 17

Graph the parabola with the given equation.
-$$( x - 1 ) ^ { 2 } = 7 ( y - 2 )$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 18

Tech: Parametric Equations
-Cycloid: $x = 2 ( t - \sin t ) , y = 2 ( 1 - \cos t ) , 0 \leq t \leq 6 \pi$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

Find the standard form of the equation of the ellipse satisfying the given conditions.
-Foci: $( - 3,0 ) , ( 3,0 ) ; x$-intercepts: $- 4$ and 4

Accepted Answer

A)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 7 } = 1$ 
B)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 7 } = 1$ 
D)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$ 
A)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 7 } = 1$ 
B)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 7 } = 1$ 
D)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

Question 20

The Parabola
1 Graph Parabolas with Vertices at the Origin
-$$y ^ { 2 } = - 24 x$$

Accepted Answer

A)  focus: $( - 6,0 )$
directrix: $x = 6$ 
B)  focus: $( 0 , - 6 )$
directrix: $y = 6$ 
C)  focus: $( 6,0 )$
directrix: $x = - 6$ 
D)  focus: $( - 6,0 )$
directrix: $\mathrm { y } = 6$ 
A)  focus: $( - 6,0 )$
directrix: $x = 6$ 
B)  focus: $( 0 , - 6 )$
directrix: $y = 6$ 
C)  focus: $( 6,0 )$
directrix: $x = - 6$ 
D)  focus: $( - 6,0 )$
directrix: $\mathrm { y } = 6$

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

Convert the equation to the standard form for an ellipse by completing the square on x and y. - $4 x ^ { 2 } + 16 y ^ { 2 } + 8 x + 96 y + 84 = 0$

Use point plotting to graph the plane curve described by the given parametric equations. - $x=5 \sin t, y=5 \cos t ; 0 \leq t \leq 2 \pi$ $Use point plotting to graph the plane curve described by the given parametric equations. - x=5 \sin t, y=5 \cos t ; 0 \leq t \leq 2 \pi$

Graph Hyperbolas Centered at the Origin - $16 x^{2}-9 y^{2}=144$ $Graph Hyperbolas Centered at the Origin - 16 x^{2}-9 y^{2}=144$

Find the standard form of the equation of the ellipse satisfying the given conditions. -Endpoints of major axis: $( 1 , - 3 )$ and $( 1,7 )$ ; endpoints of minor axis: $( - 3,2 )$ and $( 5,2 )$ ;

Graph Ellipses Not Centered at the Origin - $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$ $Graph Ellipses Not Centered at the Origin - \frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$

Tech: Rotation of Axes -

Use the rotated system to graph the equation. - $3 x^{2}-2 \sqrt{3} x y+y^{2}-8 x-8 \sqrt{3} y=0$ $Use the rotated system to graph the equation. - 3 x^{2}-2 \sqrt{3} x y+y^{2}-8 x-8 \sqrt{3} y=0$

Eliminate the Parameter - $x = \sqrt { t } , y = 2 t + 4 ; 0 \leq t \leq 4$

Match the equation to the graph. - $y ^ { 2 } = - 4 x$

The Parabola 1 Graph Parabolas with Vertices at the Origin - $y ^ { 2 } = 12 x$

Write Equations of Hyperbolas in Standard Form -Endpoints of transverse axis: $( - 5,0 ) , ( 5,0 )$ ; foci: $( - 11,0 ) , ( - 11,0 )$

Use point plotting to graph the plane curve described by the given parametric equations. - $x=2 t, y=|t-1| ;-\infty \leq t \leq \infty$ $Use point plotting to graph the plane curve described by the given parametric equations. - x=2 t, y=|t-1| ;-\infty \leq t \leq \infty$

Find a set of parametric equations for the rectangular equation. - $y = x ^ { 4 } - 3$

Write the appropriate rotation formulas so that in a rotated system the equation has no x'y'-term. - $6 x ^ { 2 } - 4 x y + 3 y ^ { 2 } - 8 x + 8 y = 0$

Tech: Rotation of Axes - $5 x^{2}+3 x y+5 y^{2}=11$ $Tech: Rotation of Axes - 5 x^{2}+3 x y+5 y^{2}=11$

Graph the parabola with the given equation. - $( x - 1 ) ^ { 2 } = 7 ( y - 2 )$ $Graph the parabola with the given equation. - ( x - 1 ) ^ { 2 } = 7 ( y - 2 )$

Tech: Parametric Equations -Cycloid: $x = 2 ( t - \sin t ) , y = 2 ( 1 - \cos t ) , 0 \leq t \leq 6 \pi$ $Tech: Parametric Equations -Cycloid: x = 2 ( t - \sin t ) , y = 2 ( 1 - \cos t ) , 0 \leq t \leq 6 \pi$

Find the standard form of the equation of the ellipse satisfying the given conditions. -Foci: $( - 3,0 ) , ( 3,0 ) ; x$ -intercepts: $- 4$ and 4

The Parabola 1 Graph Parabolas with Vertices at the Origin - $y ^ { 2 } = - 24 x$

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

Rotation of Axes 1 Identify Conics Without Completing the Square - 3x2+4y2+2x+3y=03 x ^ { 2 } + 4 y ^ { 2 } + 2 x + 3 y = 03x2+4y2+2x+3y=0

Convert the equation to the standard form for an ellipse by completing the square on x and y. - 4x2+16y2+8x+96y+84=04 x ^ { 2 } + 16 y ^ { 2 } + 8 x + 96 y + 84 = 04x2+16y2+8x+96y+84=0

Use point plotting to graph the plane curve described by the given parametric equations. - x=5sin⁡t,y=5cos⁡t;0≤t≤2πx=5 \sin t, y=5 \cos t ; 0 \leq t \leq 2 \pix=5sint,y=5cost;0≤t≤2π

Graph Hyperbolas Centered at the Origin - 16x2−9y2=14416 x^{2}-9 y^{2}=14416x2−9y2=144

Find the standard form of the equation of the ellipse satisfying the given conditions. -Endpoints of major axis: (1,−3)( 1 , - 3 )(1,−3) and (1,7)( 1,7 )(1,7) ; endpoints of minor axis: (−3,2)( - 3,2 )(−3,2) and (5,2)( 5,2 )(5,2) ;

Graph Ellipses Not Centered at the Origin - (x−2)216+(y−1)24=1\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 116(x−2)2​+4(y−1)2​=1

Tech: Rotation of Axes -

Use the rotated system to graph the equation. - 3x2−23xy+y2−8x−83y=03 x^{2}-2 \sqrt{3} x y+y^{2}-8 x-8 \sqrt{3} y=03x2−23​xy+y2−8x−83​y=0

Eliminate the Parameter - x=t,y=2t+4;0≤t≤4x = \sqrt { t } , y = 2 t + 4 ; 0 \leq t \leq 4x=t​,y=2t+4;0≤t≤4

Match the equation to the graph. - y2=−4xy ^ { 2 } = - 4 xy2=−4x

The Parabola 1 Graph Parabolas with Vertices at the Origin - y2=12xy ^ { 2 } = 12 xy2=12x

Write Equations of Hyperbolas in Standard Form -Endpoints of transverse axis: (−5,0),(5,0)( - 5,0 ) , ( 5,0 )(−5,0),(5,0) ; foci: (−11,0),(−11,0)( - 11,0 ) , ( - 11,0 )(−11,0),(−11,0)

Use point plotting to graph the plane curve described by the given parametric equations. - x=2t,y=∣t−1∣;−∞≤t≤∞x=2 t, y=|t-1| ;-\infty \leq t \leq \inftyx=2t,y=∣t−1∣;−∞≤t≤∞

Find a set of parametric equations for the rectangular equation. - y=x4−3y = x ^ { 4 } - 3y=x4−3

Write the appropriate rotation formulas so that in a rotated system the equation has no x'y'-term. - 6x2−4xy+3y2−8x+8y=06 x ^ { 2 } - 4 x y + 3 y ^ { 2 } - 8 x + 8 y = 06x2−4xy+3y2−8x+8y=0

Tech: Rotation of Axes - 5x2+3xy+5y2=115 x^{2}+3 x y+5 y^{2}=115x2+3xy+5y2=11

Graph the parabola with the given equation. - (x−1)2=7(y−2)( x - 1 ) ^ { 2 } = 7 ( y - 2 )(x−1)2=7(y−2)

Tech: Parametric Equations -Cycloid: x=2(t−sin⁡t),y=2(1−cos⁡t),0≤t≤6πx = 2 ( t - \sin t ) , y = 2 ( 1 - \cos t ) , 0 \leq t \leq 6 \pix=2(t−sint),y=2(1−cost),0≤t≤6π

Find the standard form of the equation of the ellipse satisfying the given conditions. -Foci: (−3,0),(3,0);x( - 3,0 ) , ( 3,0 ) ; x(−3,0),(3,0);x -intercepts: −4- 4−4 and 4

The Parabola 1 Graph Parabolas with Vertices at the Origin - y2=−24xy ^ { 2 } = - 24 xy2=−24x

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

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

Convert the equation to the standard form for an ellipse by completing the square on x and y. - $4 x ^ { 2 } + 16 y ^ { 2 } + 8 x + 96 y + 84 = 0$

Use point plotting to graph the plane curve described by the given parametric equations. - $x=5 \sin t, y=5 \cos t ; 0 \leq t \leq 2 \pi$ $Use point plotting to graph the plane curve described by the given parametric equations. - x=5 \sin t, y=5 \cos t ; 0 \leq t \leq 2 \pi$

Graph Hyperbolas Centered at the Origin - $16 x^{2}-9 y^{2}=144$ $Graph Hyperbolas Centered at the Origin - 16 x^{2}-9 y^{2}=144$

Find the standard form of the equation of the ellipse satisfying the given conditions. -Endpoints of major axis: $( 1 , - 3 )$ and $( 1,7 )$ ; endpoints of minor axis: $( - 3,2 )$ and $( 5,2 )$ ;

Graph Ellipses Not Centered at the Origin - $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$ $Graph Ellipses Not Centered at the Origin - \frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$

Use the rotated system to graph the equation. - $3 x^{2}-2 \sqrt{3} x y+y^{2}-8 x-8 \sqrt{3} y=0$ $Use the rotated system to graph the equation. - 3 x^{2}-2 \sqrt{3} x y+y^{2}-8 x-8 \sqrt{3} y=0$

Eliminate the Parameter - $x = \sqrt { t } , y = 2 t + 4 ; 0 \leq t \leq 4$

Match the equation to the graph. - $y ^ { 2 } = - 4 x$

The Parabola 1 Graph Parabolas with Vertices at the Origin - $y ^ { 2 } = 12 x$

Write Equations of Hyperbolas in Standard Form -Endpoints of transverse axis: $( - 5,0 ) , ( 5,0 )$ ; foci: $( - 11,0 ) , ( - 11,0 )$

Use point plotting to graph the plane curve described by the given parametric equations. - $x=2 t, y=|t-1| ;-\infty \leq t \leq \infty$ $Use point plotting to graph the plane curve described by the given parametric equations. - x=2 t, y=|t-1| ;-\infty \leq t \leq \infty$

Find a set of parametric equations for the rectangular equation. - $y = x ^ { 4 } - 3$

Write the appropriate rotation formulas so that in a rotated system the equation has no x'y'-term. - $6 x ^ { 2 } - 4 x y + 3 y ^ { 2 } - 8 x + 8 y = 0$

Tech: Rotation of Axes - $5 x^{2}+3 x y+5 y^{2}=11$ $Tech: Rotation of Axes - 5 x^{2}+3 x y+5 y^{2}=11$

Graph the parabola with the given equation. - $( x - 1 ) ^ { 2 } = 7 ( y - 2 )$ $Graph the parabola with the given equation. - ( x - 1 ) ^ { 2 } = 7 ( y - 2 )$

Tech: Parametric Equations -Cycloid: $x = 2 ( t - \sin t ) , y = 2 ( 1 - \cos t ) , 0 \leq t \leq 6 \pi$ $Tech: Parametric Equations -Cycloid: x = 2 ( t - \sin t ) , y = 2 ( 1 - \cos t ) , 0 \leq t \leq 6 \pi$

Find the standard form of the equation of the ellipse satisfying the given conditions. -Foci: $( - 3,0 ) , ( 3,0 ) ; x$ -intercepts: $- 4$ and 4

The Parabola 1 Graph Parabolas with Vertices at the Origin - $y ^ { 2 } = - 24 x$