Question 1

Additional Concepts
-$$y = x ^ { 2 } + 2 x + 4$$

Accepted Answer

A)  $\mathrm { Yes }$ 
B)  $\mathrm { No }$ 
A)  $\mathrm { Yes }$ 
B)  $\mathrm { No }$

Question 2

Find two sets of parametric equations for the given rectangular equation.
-$$y = x ^ { 2 } - 4$$

Accepted Answer

A)  $x = t , y = t ^ { 2 } - 4 ; x = \sqrt { t } , y = t - 4 , t \geq 0$ 
B)  $x = t , y = t ^ { 2 } - 4 ; x = \sqrt { t } , y = t + 4 , t \geq 0$ 
C)  $x = - t , y = t ^ { 2 } + 4 ; x = \sqrt { t } , y = t - 4$ 
D)  $x = - t , y = t ^ { 2 } - 4 ; x = \sqrt { t } , y = - t + 4 , t \geq 0$ 
A)  $x = t , y = t ^ { 2 } - 4 ; x = \sqrt { t } , y = t - 4 , t \geq 0$ 
B)  $x = t , y = t ^ { 2 } - 4 ; x = \sqrt { t } , y = t + 4 , t \geq 0$ 
C)  $x = - t , y = t ^ { 2 } + 4 ; x = \sqrt { t } , y = t - 4$ 
D)  $x = - t , y = t ^ { 2 } - 4 ; x = \sqrt { t } , y = - t + 4 , t \geq 0$

Question 3

Solve Applied Problems Involving Hyperbolas
-A satellite following the hyperbolic path shown in the picture turns rapidly at $( 0,6 )$ and then moves closer and closer to the line $y = \frac { 9 } { 2 } x$ as it gets farther from the tracking station at the origin. Find the equation that describes the path of the satellite if the center of the hyperbola is at $( 0,0 )$.

Accepted Answer

A)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { \frac { 16 } { 9 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { \left( \frac { 54 } { 4 } \right) ^ { 2 } } = 1$ 
C)  $\frac { y ^ { 2 } } { \frac { 16 } { 9 } } - \frac { x ^ { 2 } } { 36 } = 1$ 
D)  $\frac { x ^ { 2 } } { \left( \frac { 54 } { 4 } \right) ^ { 2 } } - \frac { y ^ { 2 } } { 36 } = 1$ 
A)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { \frac { 16 } { 9 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { \left( \frac { 54 } { 4 } \right) ^ { 2 } } = 1$ 
C)  $\frac { y ^ { 2 } } { \frac { 16 } { 9 } } - \frac { x ^ { 2 } } { 36 } = 1$ 
D)  $\frac { x ^ { 2 } } { \left( \frac { 54 } { 4 } \right) ^ { 2 } } - \frac { y ^ { 2 } } { 36 } = 1$

Question 4

Solve Applied Problems Involving Parabolas
-A satellite dish is in the shape of a parabolic surface. Signals coming from a satellite strike the surface of the dish and are reflected to the focus, where the receiver is located. The satellite dish shown has a diameter of 6 feet and a depth of 6 feet. The parabola is positioned in a rectangular coordinate system with its vertex at the origin. The receiver should be placed at the focus $( 0 , \mathrm { p } )$. The value of $\mathrm { p }$ is given by the equation $\mathrm { a } = \frac { 1 } { 4 \mathrm { p } }$. How far from the base of the dish should the receiver be placed?.

Accepted Answer

A)  $\frac { 3 } { 8 }$ feet from the base 
B)  $1 \frac { 1 } { 2 }$ feet from the base 
C)  $\frac { 2 } { 3 }$ feet from the base 
D)  $2 \frac { 2 } { 3 }$ feet from the base 
A)  $\frac { 3 } { 8 }$ feet from the base 
B)  $1 \frac { 1 } { 2 }$ feet from the base 
C)  $\frac { 2 } { 3 }$ feet from the base 
D)  $2 \frac { 2 } { 3 }$ feet from the base

Question 5

Additional Concepts
-$$y ^ { 2 } + 6 y - x + 11 = 0$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 6

Eliminate the Parameter
-A hyperbola: $x = 1 + 4 \sec t , y = 5 + 5$ tan $t$

Accepted Answer

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

Question 7

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

Accepted Answer

A)  $\frac { ( y + 1 ) ^ { 2 } } { 4 } - \frac { ( x - 2 ) ^ { 2 } } { 9 } = 1$ 
B)  $\frac { ( y - 1 ) ^ { 2 } } { 4 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1$ 
C)  $\frac { ( y + 1 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 4 } = 1$ 
D)  $\frac { ( x + 2 ) ^ { 2 } } { 9 } - \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$ 
A)  $\frac { ( y + 1 ) ^ { 2 } } { 4 } - \frac { ( x - 2 ) ^ { 2 } } { 9 } = 1$ 
B)  $\frac { ( y - 1 ) ^ { 2 } } { 4 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1$ 
C)  $\frac { ( y + 1 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 4 } = 1$ 
D)  $\frac { ( x + 2 ) ^ { 2 } } { 9 } - \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$

Question 8

Find the standard form of the equation of the ellipse satisfying the given conditions.
-Endpoints of major axis: $( - 7,4 )$ and $( 9,4 )$; endpoints of minor axis: $( 1 , - 1 )$ and $( 1,9 )$

Accepted Answer

A)  $\frac { ( x - 1 ) ^ { 2 } } { 64 } + \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( x - 4 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 64 } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { 64 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 0$ 
D)  $\frac { ( x + 1 ) ^ { 2 } } { 64 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 1$ 
A)  $\frac { ( x - 1 ) ^ { 2 } } { 64 } + \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( x - 4 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 64 } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { 64 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 0$ 
D)  $\frac { ( x + 1 ) ^ { 2 } } { 64 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 1$

Question 9

Use the rotated system to graph the equation.
-$7 x^{2}+2 x y+7 y^{2}=24$

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Solve Applied Problems Involving Hyperbolas
-Two recording devices are set 3200 feet apart, with the device at point A to the west of the device at point B. At a point on a line between the devices, 400 feet from point B, a small amount of explosive is detonated. The recording devices record the time the sound reaches each one. How far directly north of site B should a second explosion be done so that the measured time difference recorded by the devices is the same as that for the first detonation?

Accepted Answer

A)  $933.33$ feet 
B)  $4098.78$ feet 
C)  $1549.19$ feet 
D)  $1763.83$ feet 
A)  $933.33$ feet 
B)  $4098.78$ feet 
C)  $1549.19$ feet 
D)  $1763.83$ feet

Question 12

The Parabola
1 Graph Parabolas with Vertices at the Origin
-$$x ^ { 2 } = - 28 y$$

Accepted Answer

A)  focus: $( 0 , - 7 )$
 directrix: $y = 7$ 
B)  focus: $( - 14,0 )$
directrix: $x = 7$ 
C)  focus: $( 0 , - 7 )$
 directrix: $y = -7$ 
D)  focus: $( 0,7 )$ 
 directrix: $y = -7$ 
A)  focus: $( 0 , - 7 )$
 directrix: $y = 7$ 
B)  focus: $( - 14,0 )$
directrix: $x = 7$ 
C)  focus: $( 0 , - 7 )$
 directrix: $y = -7$ 
D)  focus: $( 0,7 )$ 
 directrix: $y = -7$

Question 13

Write the appropriate rotation formulas so that in a rotated system the equation has no x'y'-term.
-$10 x ^ { 2 } - 4 x y + 6 y ^ { 2 } - 8 x + 8 y = 0$

Accepted Answer

A)  $x = \frac { \sqrt { 2 - \sqrt { 2 } } } { 2 } x ^ { \prime } - \frac { \sqrt { 2 + \sqrt { 2 } } } { 2 } y ^ { \prime } ; y = \frac { \sqrt { 2 + \sqrt { 2 } } } { 2 } x ^ { \prime } + \frac { \sqrt { 2 - \sqrt { 2 } } } { 2 } y ^ { \prime }$ 
B)  $x = \frac { \sqrt { 2 } } { 2 } \left( x ^ { \prime } - y ^ { \prime } \right) ; y = \frac { \sqrt { 2 } } { 2 } \left( x ^ { \prime } + y ^ { \prime } \right)$ 
C)  $x = - y ^ { \prime } ; y = x ^ { \prime }$ 
D)  $x = \frac { 1 } { 2 } x ^ { \prime } - \frac { \sqrt { 3 } } { 2 } y ^ { \prime } ; y = \frac { \sqrt { 3 } } { 2 } x ^ { \prime } + \frac { 1 } { 2 } y ^ { \prime }$ 
A)  $x = \frac { \sqrt { 2 - \sqrt { 2 } } } { 2 } x ^ { \prime } - \frac { \sqrt { 2 + \sqrt { 2 } } } { 2 } y ^ { \prime } ; y = \frac { \sqrt { 2 + \sqrt { 2 } } } { 2 } x ^ { \prime } + \frac { \sqrt { 2 - \sqrt { 2 } } } { 2 } y ^ { \prime }$ 
B)  $x = \frac { \sqrt { 2 } } { 2 } \left( x ^ { \prime } - y ^ { \prime } \right) ; y = \frac { \sqrt { 2 } } { 2 } \left( x ^ { \prime } + y ^ { \prime } \right)$ 
C)  $x = - y ^ { \prime } ; y = x ^ { \prime }$ 
D)  $x = \frac { 1 } { 2 } x ^ { \prime } - \frac { \sqrt { 3 } } { 2 } y ^ { \prime } ; y = \frac { \sqrt { 3 } } { 2 } x ^ { \prime } + \frac { 1 } { 2 } y ^ { \prime }$

Question 14

Additional Concepts
-$24 x y - 7 y ^ { 2 } + 36 = 0 ;$ Find the equations of the asymptotes.

Accepted Answer

A)  $y ^ { \prime } = - \frac { 4 } { 3 } x ^ { \prime }$ and $y ^ { \prime } = \frac { 4 } { 3 } x ^ { \prime }$ 
B)  $y ^ { \prime } = - \frac { 3 } { 4 } x ^ { \prime }$ and $y ^ { \prime } = \frac { 3 } { 4 } x ^ { \prime }$ 
C)  $y ^ { \prime } = - \frac { 2 } { 3 } x ^ { \prime }$ and $y ^ { \prime } = \frac { 2 } { 3 } x ^ { \prime }$ 
D)  $y ^ { \prime } = - \frac { x ^ { \prime } } { 3 }$ and $y ^ { \prime } = \frac { x ^ { \prime } } { 3 }$ 
A)  $y ^ { \prime } = - \frac { 4 } { 3 } x ^ { \prime }$ and $y ^ { \prime } = \frac { 4 } { 3 } x ^ { \prime }$ 
B)  $y ^ { \prime } = - \frac { 3 } { 4 } x ^ { \prime }$ and $y ^ { \prime } = \frac { 3 } { 4 } x ^ { \prime }$ 
C)  $y ^ { \prime } = - \frac { 2 } { 3 } x ^ { \prime }$ and $y ^ { \prime } = \frac { 2 } { 3 } x ^ { \prime }$ 
D)  $y ^ { \prime } = - \frac { x ^ { \prime } } { 3 }$ and $y ^ { \prime } = \frac { x ^ { \prime } } { 3 }$

Question 15

Graph the parabola with the given equation.
-$$( y + 2 ) ^ { 2 } = - 8 ( x - 2 )$$

Accepted Answer

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

Question 16

Find the standard form of the equation of the ellipse satisfying the given conditions.
-Major axis vertical with length $12 ;$ length of minor axis $= 6 ;$ center $( 0,0 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 1$ 
B)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 36 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 144 } = 1$ 
A)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 1$ 
B)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 36 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 144 } = 1$

Question 17

Use point plotting to graph the plane curve described by the given parametric equations.
-$x=2 t-1, y=t^{2}+6 ;-4 \leq t \leq 4$

Accepted Answer

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

Question 18

Graph the parabola.
-$y^{2}=12 x$

Accepted Answer

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

Question 19

Match the equation to the graph.
-$$x ^ { 2 } = 9 y$$

Accepted Answer

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

Question 20

Write the word or phrase that best completes each statement or answers the question. The parametric equations of four curves are given. Graph each of them, indicating the orientation.
-$$\begin{array} { l } 
C _ { 1 } : x = 7 \sin t , y = 7 - 7 \cos ^ { 2 } t ; \frac { \pi } { 2 } \leq t \leq \frac { 3 \pi } { 2 } \
C _ { 2 } : x = \ln t , y = \ln t ^ { 2 } ; e ^ { - 4 } \leq t \leq e ^ { 3 } \
C _ { 3 } : x = t ^ { 2 } - 8 , y = t - 3 ; - 4 \leq t \leq 4 \
C _ { 4 } : x = t - 5 , y = t + 2 ; - 4 \leq t \leq 7
\end{array}$$

Accepted Answer

The answer of Write the word or phrase that best...

Additional Concepts - $y = x ^ { 2 } + 2 x + 4$

Find two sets of parametric equations for the given rectangular equation. - $y = x ^ { 2 } - 4$

Additional Concepts - $y ^ { 2 } + 6 y - x + 11 = 0$

Eliminate the Parameter -A hyperbola: $x = 1 + 4 \sec t , y = 5 + 5$ tan $t$

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

Find the standard form of the equation of the ellipse satisfying the given conditions. -Endpoints of major axis: $( - 7,4 )$ and $( 9,4 )$ ; endpoints of minor axis: $( 1 , - 1 )$ and $( 1,9 )$

Use the rotated system to graph the equation. - $7 x^{2}+2 x y+7 y^{2}=24$ $Use the rotated system to graph the equation. - 7 x^{2}+2 x y+7 y^{2}=24$

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

The Parabola 1 Graph Parabolas with Vertices at the Origin - $x ^ { 2 } = - 28 y$

Write the appropriate rotation formulas so that in a rotated system the equation has no x'y'-term. - $10 x ^ { 2 } - 4 x y + 6 y ^ { 2 } - 8 x + 8 y = 0$

Additional Concepts - $24 x y - 7 y ^ { 2 } + 36 = 0 ;$ Find the equations of the asymptotes.

Graph the parabola with the given equation. - $( y + 2 ) ^ { 2 } = - 8 ( x - 2 )$ $Graph the parabola with the given equation. - ( y + 2 ) ^ { 2 } = - 8 ( x - 2 )$

Find the standard form of the equation of the ellipse satisfying the given conditions. -Major axis vertical with length $12 ;$ length of minor axis $= 6 ;$ center $( 0,0 )$

Use point plotting to graph the plane curve described by the given parametric equations. - $x=2 t-1, y=t^{2}+6 ;-4 \leq t \leq 4$ $Use point plotting to graph the plane curve described by the given parametric equations. - x=2 t-1, y=t^{2}+6 ;-4 \leq t \leq 4$

Graph the parabola. - $y^{2}=12 x$ $Graph the parabola. - y^{2}=12 x$

Match the equation to the graph. - $x ^ { 2 } = 9 y$

Write the word or phrase that best completes each statement or answers the question. The parametric equations of four curves are given. Graph each of them, indicating the orientation. - :x=7t,y=7-7t;\leqt\leq :x=t,y=;\leqt\leq :x=-8,y=t-3;-4\leqt\leq4 :x=t-5,y=t+2;-4\leqt\leq7

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 - y=x2+2x+4y = x ^ { 2 } + 2 x + 4y=x2+2x+4

Find two sets of parametric equations for the given rectangular equation. - y=x2−4y = x ^ { 2 } - 4y=x2−4

Additional Concepts - y2+6y−x+11=0y ^ { 2 } + 6 y - x + 11 = 0y2+6y−x+11=0

Eliminate the Parameter -A hyperbola: x=1+4sec⁡t,y=5+5x = 1 + 4 \sec t , y = 5 + 5x=1+4sect,y=5+5 tan ttt

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

Find the standard form of the equation of the ellipse satisfying the given conditions. -Endpoints of major axis: (−7,4)( - 7,4 )(−7,4) and (9,4)( 9,4 )(9,4) ; endpoints of minor axis: (1,−1)( 1 , - 1 )(1,−1) and (1,9)( 1,9 )(1,9)

Use the rotated system to graph the equation. - 7x2+2xy+7y2=247 x^{2}+2 x y+7 y^{2}=247x2+2xy+7y2=24

Graph Ellipses Not Centered at the Origin - (x+2)29+(y−2)216=1\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 19(x+2)2​+16(y−2)2​=1

The Parabola 1 Graph Parabolas with Vertices at the Origin - x2=−28yx ^ { 2 } = - 28 yx2=−28y

Write the appropriate rotation formulas so that in a rotated system the equation has no x'y'-term. - 10x2−4xy+6y2−8x+8y=010 x ^ { 2 } - 4 x y + 6 y ^ { 2 } - 8 x + 8 y = 010x2−4xy+6y2−8x+8y=0

Additional Concepts - 24xy−7y2+36=0;24 x y - 7 y ^ { 2 } + 36 = 0 ;24xy−7y2+36=0; Find the equations of the asymptotes.

Graph the parabola with the given equation. - (y+2)2=−8(x−2)( y + 2 ) ^ { 2 } = - 8 ( x - 2 )(y+2)2=−8(x−2)

Find the standard form of the equation of the ellipse satisfying the given conditions. -Major axis vertical with length 12;12 ;12; length of minor axis =6;= 6 ;=6; center (0,0)( 0,0 )(0,0)

Use point plotting to graph the plane curve described by the given parametric equations. - x=2t−1,y=t2+6;−4≤t≤4x=2 t-1, y=t^{2}+6 ;-4 \leq t \leq 4x=2t−1,y=t2+6;−4≤t≤4

Graph the parabola. - y2=12xy^{2}=12 xy2=12x

Match the equation to the graph. - x2=9yx ^ { 2 } = 9 yx2=9y

Write the word or phrase that best completes each statement or answers the question. The parametric equations of four curves are given. Graph each of them, indicating the orientation. - :x=7t,y=7-7t;\leqt\leq :x=t,y=;\leqt\leq :x=-8,y=t-3;-4\leqt\leq4 :x=t-5,y=t+2;-4\leqt\leq7

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 - $y = x ^ { 2 } + 2 x + 4$

Find two sets of parametric equations for the given rectangular equation. - $y = x ^ { 2 } - 4$

Additional Concepts - $y ^ { 2 } + 6 y - x + 11 = 0$

Eliminate the Parameter -A hyperbola: $x = 1 + 4 \sec t , y = 5 + 5$ tan $t$

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

Find the standard form of the equation of the ellipse satisfying the given conditions. -Endpoints of major axis: $( - 7,4 )$ and $( 9,4 )$ ; endpoints of minor axis: $( 1 , - 1 )$ and $( 1,9 )$

Use the rotated system to graph the equation. - $7 x^{2}+2 x y+7 y^{2}=24$ $Use the rotated system to graph the equation. - 7 x^{2}+2 x y+7 y^{2}=24$

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

The Parabola 1 Graph Parabolas with Vertices at the Origin - $x ^ { 2 } = - 28 y$

Write the appropriate rotation formulas so that in a rotated system the equation has no x'y'-term. - $10 x ^ { 2 } - 4 x y + 6 y ^ { 2 } - 8 x + 8 y = 0$

Additional Concepts - $24 x y - 7 y ^ { 2 } + 36 = 0 ;$ Find the equations of the asymptotes.

Graph the parabola with the given equation. - $( y + 2 ) ^ { 2 } = - 8 ( x - 2 )$ $Graph the parabola with the given equation. - ( y + 2 ) ^ { 2 } = - 8 ( x - 2 )$

Find the standard form of the equation of the ellipse satisfying the given conditions. -Major axis vertical with length $12 ;$ length of minor axis $= 6 ;$ center $( 0,0 )$

Use point plotting to graph the plane curve described by the given parametric equations. - $x=2 t-1, y=t^{2}+6 ;-4 \leq t \leq 4$ $Use point plotting to graph the plane curve described by the given parametric equations. - x=2 t-1, y=t^{2}+6 ;-4 \leq t \leq 4$

Graph the parabola. - $y^{2}=12 x$ $Graph the parabola. - y^{2}=12 x$

Match the equation to the graph. - $x ^ { 2 } = 9 y$