Question 1

Write Equations of Parabolas in Standard Form
-Vertex: $( 8 , - 6 )$; Focus: $( 8 , - 7 )$

Accepted Answer

A)  $( x - 8 ) ^ { 2 } = - 4 ( y + 6 )$ 
B)  $( x - 8 ) ^ { 2 } = 4 ( y + 6 )$ 
C)  $( y - 6 ) ^ { 2 } = - 4 ( x + 8 )$ 
D)  $( y - 6 ) ^ { 2 } = 4 ( x + 8 )$ 
A)  $( x - 8 ) ^ { 2 } = - 4 ( y + 6 )$ 
B)  $( x - 8 ) ^ { 2 } = 4 ( y + 6 )$ 
C)  $( y - 6 ) ^ { 2 } = - 4 ( x + 8 )$ 
D)  $( y - 6 ) ^ { 2 } = 4 ( x + 8 )$

Question 2

Tech: Conic Sections in Polar Coordinates
-$r=\frac{2}{2+2 \sin \left(\theta+\frac{\pi}{6}\right)}$

Accepted Answer

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

Question 3

Graph Ellipses Not Centered at the Origin
-$$\frac { ( \mathrm { x } + 1 ) ^ { 2 } } { 36 } + \frac { ( \mathrm { y } + 3 ) ^ { 2 } } { 9 } = 1$$

Accepted Answer

A)  foci at $( - 1 + 3 \sqrt { 3 } , - 3 )$ and $( - 1 - 3 \sqrt { 3 } , - 3 )$ 
B)  foci at $( - 3 + 3 \sqrt { 3 } , - 1 )$ and $( - 3 - 3 \sqrt { 3 } , - 1 )$ 
C)  foci at $( - 3 \sqrt { 3 } , - 3 )$ and $( 3 \sqrt { 3 } , - 3 )$ 
D)  foci at $( - 1 + 3 \sqrt { 3 } , - 1 )$ and $( - 1 - 3 \sqrt { 3 } , - 1 )$ 
A)  foci at $( - 1 + 3 \sqrt { 3 } , - 3 )$ and $( - 1 - 3 \sqrt { 3 } , - 3 )$ 
B)  foci at $( - 3 + 3 \sqrt { 3 } , - 1 )$ and $( - 3 - 3 \sqrt { 3 } , - 1 )$ 
C)  foci at $( - 3 \sqrt { 3 } , - 3 )$ and $( 3 \sqrt { 3 } , - 3 )$ 
D)  foci at $( - 1 + 3 \sqrt { 3 } , - 1 )$ and $( - 1 - 3 \sqrt { 3 } , - 1 )$

Question 4

Eliminate the Parameter
-$\mathrm { x } = \mathrm { e } ^ { \mathrm { t } } , \mathrm { y } = \mathrm { e } ^ { - \mathrm { t } } ; - \infty < \mathrm { t } < \infty$

Accepted Answer

A)  $\mathrm { y } = \mathrm { e } ^ { - \ln x ; } 0 < \mathrm { x } < \infty$ 
B)  $\mathrm { y } = \mathrm { e } ^ { \ln \mathrm { x } ; 0 < \mathrm { x } < \infty }$ 
C)  $\mathrm { y } = \mathrm { e } ^ { \mathrm { x } } ; - \infty < \mathrm { x } < \infty$ 
D)  $\mathrm { y } = \mathrm { e } ^ { - \mathrm { x } } ; - \infty < \mathrm { x } < \infty$ Eliminate the parameter. Write the resulting equation in standard form. 
A)  $\mathrm { y } = \mathrm { e } ^ { - \ln x ; } 0 < \mathrm { x } < \infty$ 
B)  $\mathrm { y } = \mathrm { e } ^ { \ln \mathrm { x } ; 0 < \mathrm { x } < \infty }$ 
C)  $\mathrm { y } = \mathrm { e } ^ { \mathrm { x } } ; - \infty < \mathrm { x } < \infty$ 
D)  $\mathrm { y } = \mathrm { e } ^ { - \mathrm { x } } ; - \infty < \mathrm { x } < \infty$ Eliminate the parameter. Write the resulting equation in standard form.

Question 5

Graph Parabolas with Vertices Not at the Origin
-$$( x + 2 ) ^ { 2 } = 8 ( y - 3 )$$

Accepted Answer

A)  vertex: $( - 2,3 )$
focus: $( - 2,5 )$
directrix: $y = 1$ 
B)  vertex: $( 2 , - 3 )$
focus: $( 2 , - 1 )$
directrix: $y = - 5$ 
C)  vertex: $( 3 , - 2 )$
focus: $( 3,0 )$
directrix: $y = - 4$ 
D)  vertex: $( - 2,3 )$
focus: $( - 2,1 )$
directrix: $x = 5$ 
A)  vertex: $( - 2,3 )$
focus: $( - 2,5 )$
directrix: $y = 1$ 
B)  vertex: $( 2 , - 3 )$
focus: $( 2 , - 1 )$
directrix: $y = - 5$ 
C)  vertex: $( 3 , - 2 )$
focus: $( 3,0 )$
directrix: $y = - 4$ 
D)  vertex: $( - 2,3 )$
focus: $( - 2,1 )$
directrix: $x = 5$

Question 6

Understand the Advantages of Parametric Representations
-Ron throws a ball straight up with an initial velocity of 40 feet per second from a height of 5 feet. Find parametric equations that describe the motion of the ball as a function of time. How long is the ball in the air? When is the ball at its maximum height? What is the maximum height of the ball?

Accepted Answer

A)  $x = 0 ; y = - 16 t ^ { 2 } + 40 t + 5$;
$2.619 \mathrm { sec } ;$
$1.25 \mathrm { sec } ;$
$30$ feet 
B)  $x = 0 ; y = - 16 t ^ { 2 } + 40 t + 5$;
$5.239 \mathrm { sec } ;$
$1.25 \mathrm { sec } ;$
$25$ feet 
C)  $x = 0 ; y = - 16 t ^ { 2 } + 40 t + 5 ;$
$2.368 \mathrm { sec }$
$1.25 \mathrm { sec } ;$
$5.001$ feet 
D)  $x = 0 ; y = - 16 t ^ { 2 } + 40 t + 5$;
$4.736 \mathrm { sec } ;$
$1.25 \mathrm { sec } ;$
$184.439$ feet 
A)  $x = 0 ; y = - 16 t ^ { 2 } + 40 t + 5$;
$2.619 \mathrm { sec } ;$
$1.25 \mathrm { sec } ;$
$30$ feet 
B)  $x = 0 ; y = - 16 t ^ { 2 } + 40 t + 5$;
$5.239 \mathrm { sec } ;$
$1.25 \mathrm { sec } ;$
$25$ feet 
C)  $x = 0 ; y = - 16 t ^ { 2 } + 40 t + 5 ;$
$2.368 \mathrm { sec }$
$1.25 \mathrm { sec } ;$
$5.001$ feet 
D)  $x = 0 ; y = - 16 t ^ { 2 } + 40 t + 5$;
$4.736 \mathrm { sec } ;$
$1.25 \mathrm { sec } ;$
$184.439$ feet

Question 7

Graph the ellipse and locate the foci.
-$$\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } = 1$$

Accepted Answer

A)  foci at $( 0,3 )$ and $( 0 , - 3 )$
  
B)  foci at $( 3,0 )$ and $( - 3,0 )$
  
C)  foci at $( 2 \sqrt { 5 } , 0 )$ and $( - 2 \sqrt { 5 } , 0 )$
  
D)  foci at $( 0,2 \sqrt { 5 } )$ and $( 0 , - 2 \sqrt { 5 } )$
  
A)  foci at $( 0,3 )$ and $( 0 , - 3 )$
  
B)  foci at $( 3,0 )$ and $( - 3,0 )$
  
C)  foci at $( 2 \sqrt { 5 } , 0 )$ and $( - 2 \sqrt { 5 } , 0 )$
  
D)  foci at $( 0,2 \sqrt { 5 } )$ and $( 0 , - 2 \sqrt { 5 } )$

Question 8

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.
-$$\begin{aligned}
( y - 6 ) ^ { 2 } & = x + 36 \
y & = - \frac { 1 } { 6 } x
\end{aligned}$$

Accepted Answer

A)  $\{ ( - 36,6 ) , ( 0,0 ) \}$ 
B)  $\{ ( 36 , - 6 ) , ( 0,0 ) \}$ 
C)  $\{ ( - 36,0 ) , ( 6,0 ) \}$ 
D)  $\{ ( - 36,6 ) \}$ 
A)  $\{ ( - 36,6 ) , ( 0,0 ) \}$ 
B)  $\{ ( 36 , - 6 ) , ( 0,0 ) \}$ 
C)  $\{ ( - 36,0 ) , ( 6,0 ) \}$ 
D)  $\{ ( - 36,6 ) \}$

Question 9

Parametric Equations
1 Use Point Plotting to Graph Plane Curves Described by Parametric Equations
-$x = t ^ { 2 } + 1 , y = 6 - t ^ { 3 } ; t = 2$

Accepted Answer

A)  $( 5 , - 2 )$ 
B)  $( 5,14 )$ 
C)  $( 10 , - 7 )$ 
D)  $( 10,0 )$ 
A)  $( 5 , - 2 )$ 
B)  $( 5,14 )$ 
C)  $( 10 , - 7 )$ 
D)  $( 10,0 )$

Question 10

Conic Sections in Polar Coordinates
1 Define Conics in Terms of a Focus and a Directrix
-$$r = \frac { 6 } { 1 - 2 \cos \theta }$$

Accepted Answer

A)  hyperbola; The directrix is 3 unit(s) to the left of the pole at $x = - 3$. 
B)  hyperbola; The directrix is 3 unit(s) to the right of the pole at $x = 3$. 
C)  ellipse; The directrix is 3 unit(s) to the left of the pole at $x = - 3$. 
D)  ellipse; The directrix is 3 unit(s) to the right of the pole at $x = 3$. 
A)  hyperbola; The directrix is 3 unit(s) to the left of the pole at $x = - 3$. 
B)  hyperbola; The directrix is 3 unit(s) to the right of the pole at $x = 3$. 
C)  ellipse; The directrix is 3 unit(s) to the left of the pole at $x = - 3$. 
D)  ellipse; The directrix is 3 unit(s) to the right of the pole at $x = 3$.

Question 11

Write Equations of Parabolas in Standard Form
-Vertex: $( 2 , - 1 )$; Focus: $( 5 , - 1 )$

Accepted Answer

A)  $( \mathrm { y } + 1 ) ^ { 2 } = 12 ( \mathrm { x } - 2 )$ 
B)  $( y + 1 ) ^ { 2 } = - 12 ( x - 2 )$ 
C)  $( x + 2 ) ^ { 2 } = - 16 ( y - 1 )$ 
D)  $( x + 2 ) ^ { 2 } = 16 ( y - 1 )$ 
A)  $( \mathrm { y } + 1 ) ^ { 2 } = 12 ( \mathrm { x } - 2 )$ 
B)  $( y + 1 ) ^ { 2 } = - 12 ( x - 2 )$ 
C)  $( x + 2 ) ^ { 2 } = - 16 ( y - 1 )$ 
D)  $( x + 2 ) ^ { 2 } = 16 ( y - 1 )$

Question 12

Find the standard form of the equation of the ellipse satisfying the given conditions.
-Foci: $( 0 , - 4 ) , ( 0,4 ) ; y$-intercepts: $- 8$ and 8

Accepted Answer

A)  $\frac { x ^ { 2 } } { 48 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 48 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 48 } = 1$ 
D)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$ 
A)  $\frac { x ^ { 2 } } { 48 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 48 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 48 } = 1$ 
D)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$

Question 13

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

Accepted Answer

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

Question 14

Additional Concepts
-$$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 145 \
x + y = 17
\end{array} \right.$$

Accepted Answer

A)  $\{ ( 9,8 ) , ( 8,9 ) \}$ 
B)  $\{ ( - 9,8 ) , ( - 8,9 ) \}$ 
C)  $\{ ( 9 , - 8 ) , ( 8 , - 9 ) \}$ 
D)  $\{ ( - 9 , - 8 ) , ( - 8 , - 9 ) \}$ 
A)  $\{ ( 9,8 ) , ( 8,9 ) \}$ 
B)  $\{ ( - 9,8 ) , ( - 8,9 ) \}$ 
C)  $\{ ( 9 , - 8 ) , ( 8 , - 9 ) \}$ 
D)  $\{ ( - 9 , - 8 ) , ( - 8 , - 9 ) \}$

Question 15

Match the equation to the graph.
-$$y ^ { 2 } = 3 x$$

Accepted Answer

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

Question 16

Graph the parabola.
-$$y ^ { 2 } = - 5 x$$

Accepted Answer

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

Question 17

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 stand 80 inches apart. At a point between the towers and 20 inches along the road from the base of one tower, the cable is 4 inches above the roadway. Find the height of the towers.

Accepted Answer

A)  16 in. 
B)  16.5 in. 
C)  15.5 in. 
D)  18 in. 
A)  16 in. 
B)  16.5 in. 
C)  15.5 in. 
D)  18 in.

Question 18

Identify Conics Without Rotating Axes
-$$4 x ^ { 2 } - 8 x y + 4 y ^ { 2 } - 3 x + 6 = 0$$

Accepted Answer

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

Question 19

Eliminate the Parameter
-$x = 3 \tan t , y = 4 \sec t ; 0 \leq t \leq 2 \pi$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 1 ; - \infty < x < \infty$ 
B)  $\frac { y ^ { 2 } } { 16 } + \frac { x ^ { 2 } } { 9 } = 1 ; - \infty < x < \infty$ 
C)  $y = 4 \sqrt { 1 + \frac { x ^ { 2 } } { 9 } } ; - \infty < x < \infty$ 
D)  $y = x ^ { 2 } - 9 ; - 3 \leq x \leq 3$ 
A)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 1 ; - \infty < x < \infty$ 
B)  $\frac { y ^ { 2 } } { 16 } + \frac { x ^ { 2 } } { 9 } = 1 ; - \infty < x < \infty$ 
C)  $y = 4 \sqrt { 1 + \frac { x ^ { 2 } } { 9 } } ; - \infty < x < \infty$ 
D)  $y = x ^ { 2 } - 9 ; - 3 \leq x \leq 3$

Question 20

Graph the parabola with the given equation.
-$$( y + 2 ) ^ { 2 } = 8 ( x - 1 )$$

Accepted Answer

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

Write Equations of Parabolas in Standard Form -Vertex: $( 8 , - 6 )$ ; Focus: $( 8 , - 7 )$

Tech: Conic Sections in Polar Coordinates - $r=\frac{2}{2+2 \sin \left(\theta+\frac{\pi}{6}\right)}$ $Tech: Conic Sections in Polar Coordinates - r=\frac{2}{2+2 \sin \left(\theta+\frac{\pi}{6}\right)}$

Graph Ellipses Not Centered at the Origin - $\frac { ( \mathrm { x } + 1 ) ^ { 2 } } { 36 } + \frac { ( \mathrm { y } + 3 ) ^ { 2 } } { 9 } = 1$

Eliminate the Parameter - $\mathrm { x } = \mathrm { e } ^ { \mathrm { t } } , \mathrm { y } = \mathrm { e } ^ { - \mathrm { t } } ; - \infty < \mathrm { t } < \infty$

Graph Parabolas with Vertices Not at the Origin - $( x + 2 ) ^ { 2 } = 8 ( y - 3 )$

Graph the ellipse and locate the foci. - $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } = 1$ $Graph the ellipse and locate the foci. - \frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } = 1$

Parametric Equations 1 Use Point Plotting to Graph Plane Curves Described by Parametric Equations - $x = t ^ { 2 } + 1 , y = 6 - t ^ { 3 } ; t = 2$

Conic Sections in Polar Coordinates 1 Define Conics in Terms of a Focus and a Directrix - $r = \frac { 6 } { 1 - 2 \cos \theta }$

Write Equations of Parabolas in Standard Form -Vertex: $( 2 , - 1 )$ ; Focus: $( 5 , - 1 )$

Find the standard form of the equation of the ellipse satisfying the given conditions. -Foci: $( 0 , - 4 ) , ( 0,4 ) ; y$ -intercepts: $- 8$ and 8

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

Additional Concepts - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 145 \\x + y = 17\end{array} \right.$ $Additional Concepts - \left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 145 \\ x + y = 17 \end{array} \right.$

Match the equation to the graph. - $y ^ { 2 } = 3 x$

Graph the parabola. - $y ^ { 2 } = - 5 x$ $Graph the parabola. - y ^ { 2 } = - 5 x$

Identify Conics Without Rotating Axes - $4 x ^ { 2 } - 8 x y + 4 y ^ { 2 } - 3 x + 6 = 0$

Eliminate the Parameter - $x = 3 \tan t , y = 4 \sec t ; 0 \leq t \leq 2 \pi$

Graph the parabola with the given equation. - $( y + 2 ) ^ { 2 } = 8 ( x - 1 )$ $Graph the parabola with the given equation. - ( y + 2 ) ^ { 2 } = 8 ( x - 1 )$

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

Write Equations of Parabolas in Standard Form -Vertex: (8,−6)( 8 , - 6 )(8,−6) ; Focus: (8,−7)( 8 , - 7 )(8,−7)

Tech: Conic Sections in Polar Coordinates - r=22+2sin⁡(θ+π6)r=\frac{2}{2+2 \sin \left(\theta+\frac{\pi}{6}\right)}r=2+2sin(θ+6π​)2​

Graph Ellipses Not Centered at the Origin - (x+1)236+(y+3)29=1\frac { ( \mathrm { x } + 1 ) ^ { 2 } } { 36 } + \frac { ( \mathrm { y } + 3 ) ^ { 2 } } { 9 } = 136(x+1)2​+9(y+3)2​=1

Eliminate the Parameter - x=et,y=e−t;−∞<t<∞\mathrm { x } = \mathrm { e } ^ { \mathrm { t } } , \mathrm { y } = \mathrm { e } ^ { - \mathrm { t } } ; - \infty < \mathrm { t } < \inftyx=et,y=e−t;−∞<t<∞

Graph Parabolas with Vertices Not at the Origin - (x+2)2=8(y−3)( x + 2 ) ^ { 2 } = 8 ( y - 3 )(x+2)2=8(y−3)

Graph the ellipse and locate the foci. - x216+y225=1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } = 116x2​+25y2​=1

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. - (y-6 =x+36 y =-x

Parametric Equations 1 Use Point Plotting to Graph Plane Curves Described by Parametric Equations - x=t2+1,y=6−t3;t=2x = t ^ { 2 } + 1 , y = 6 - t ^ { 3 } ; t = 2x=t2+1,y=6−t3;t=2

Conic Sections in Polar Coordinates 1 Define Conics in Terms of a Focus and a Directrix - r=61−2cos⁡θr = \frac { 6 } { 1 - 2 \cos \theta }r=1−2cosθ6​

Write Equations of Parabolas in Standard Form -Vertex: (2,−1)( 2 , - 1 )(2,−1) ; Focus: (5,−1)( 5 , - 1 )(5,−1)

Find the standard form of the equation of the ellipse satisfying the given conditions. -Foci: (0,−4),(0,4);y( 0 , - 4 ) , ( 0,4 ) ; y(0,−4),(0,4);y -intercepts: −8- 8−8 and 8

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

Additional Concepts - {x2+y2=145x+y=17\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 145 \\x + y = 17\end{array} \right.{x2+y2=145x+y=17​

Match the equation to the graph. - y2=3xy ^ { 2 } = 3 xy2=3x

Graph the parabola. - y2=−5xy ^ { 2 } = - 5 xy2=−5x

Identify Conics Without Rotating Axes - 4x2−8xy+4y2−3x+6=04 x ^ { 2 } - 8 x y + 4 y ^ { 2 } - 3 x + 6 = 04x2−8xy+4y2−3x+6=0

Eliminate the Parameter - x=3tan⁡t,y=4sec⁡t;0≤t≤2πx = 3 \tan t , y = 4 \sec t ; 0 \leq t \leq 2 \pix=3tant,y=4sect;0≤t≤2π

Graph the parabola with the given equation. - (y+2)2=8(x−1)( y + 2 ) ^ { 2 } = 8 ( x - 1 )(y+2)2=8(x−1)

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

Write Equations of Parabolas in Standard Form -Vertex: $( 8 , - 6 )$ ; Focus: $( 8 , - 7 )$

Tech: Conic Sections in Polar Coordinates - $r=\frac{2}{2+2 \sin \left(\theta+\frac{\pi}{6}\right)}$ $Tech: Conic Sections in Polar Coordinates - r=\frac{2}{2+2 \sin \left(\theta+\frac{\pi}{6}\right)}$

Graph Ellipses Not Centered at the Origin - $\frac { ( \mathrm { x } + 1 ) ^ { 2 } } { 36 } + \frac { ( \mathrm { y } + 3 ) ^ { 2 } } { 9 } = 1$

Eliminate the Parameter - $\mathrm { x } = \mathrm { e } ^ { \mathrm { t } } , \mathrm { y } = \mathrm { e } ^ { - \mathrm { t } } ; - \infty < \mathrm { t } < \infty$

Graph Parabolas with Vertices Not at the Origin - $( x + 2 ) ^ { 2 } = 8 ( y - 3 )$

Graph the ellipse and locate the foci. - $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } = 1$ $Graph the ellipse and locate the foci. - \frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } = 1$

Parametric Equations 1 Use Point Plotting to Graph Plane Curves Described by Parametric Equations - $x = t ^ { 2 } + 1 , y = 6 - t ^ { 3 } ; t = 2$

Conic Sections in Polar Coordinates 1 Define Conics in Terms of a Focus and a Directrix - $r = \frac { 6 } { 1 - 2 \cos \theta }$

Write Equations of Parabolas in Standard Form -Vertex: $( 2 , - 1 )$ ; Focus: $( 5 , - 1 )$

Find the standard form of the equation of the ellipse satisfying the given conditions. -Foci: $( 0 , - 4 ) , ( 0,4 ) ; y$ -intercepts: $- 8$ and 8

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

Additional Concepts - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 145 \\x + y = 17\end{array} \right.$ $Additional Concepts - \left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 145 \\ x + y = 17 \end{array} \right.$

Match the equation to the graph. - $y ^ { 2 } = 3 x$

Graph the parabola. - $y ^ { 2 } = - 5 x$ $Graph the parabola. - y ^ { 2 } = - 5 x$

Identify Conics Without Rotating Axes - $4 x ^ { 2 } - 8 x y + 4 y ^ { 2 } - 3 x + 6 = 0$

Eliminate the Parameter - $x = 3 \tan t , y = 4 \sec t ; 0 \leq t \leq 2 \pi$

Graph the parabola with the given equation. - $( y + 2 ) ^ { 2 } = 8 ( x - 1 )$ $Graph the parabola with the given equation. - ( y + 2 ) ^ { 2 } = 8 ( x - 1 )$