Question 1

A) $y = 20 x ^ { 2 }$

Accepted Answer

B)  $x = 20 y ^ { 2 }$ 
C)  $x ^ { 2 } = 20 y$ 
D)  $y ^ { 2 } = 20 x$
-Vertex at (0, 0); axis of symmetry the x-axis; containing the point (9, 5) 
A)  $y ^ { 2 } = \frac { 25 } { 36 } x$ 
B)  $y ^ { 2 } = \frac { 25 } { 9 } x$ 
C)  $x ^ { 2 } = \frac { 25 } { 36 } y$ 
D)  $x ^ { 2 } = \frac { 25 } { 9 } y$ 
B)  $x = 20 y ^ { 2 }$ 
C)  $x ^ { 2 } = 20 y$ 
D)  $y ^ { 2 } = 20 x$
-Vertex at (0, 0); axis of symmetry the x-axis; containing the point (9, 5) 
A)  $y ^ { 2 } = \frac { 25 } { 36 } x$ 
B)  $y ^ { 2 } = \frac { 25 } { 9 } x$ 
C)  $x ^ { 2 } = \frac { 25 } { 36 } y$ 
D)  $x ^ { 2 } = \frac { 25 } { 9 } y$

Question 2

Find parametric equations for the rectangular equation.
-$y=4 x-5$

Accepted Answer

A)  $\mathrm { y } = 4 \mathrm { t } , 4 \mathrm { x } = \mathrm { t } + 5 ; 0 \leq \mathrm { t } < \infty$ 
B)  $\mathrm { x } = \frac { \mathrm { t } } { 4 } , \mathrm { y } = \mathrm { t } - \frac { 5 } { 4 } ; 0 \leq \mathrm { t } < \infty$ 
C)  $x = t , y = 4 t - 5 ; 0 \leq t < \infty$ 
D)  $x = t , y = 4 t ^ { 2 } - 5 ; 0 \leq t < \infty$ 
A)  $\mathrm { y } = 4 \mathrm { t } , 4 \mathrm { x } = \mathrm { t } + 5 ; 0 \leq \mathrm { t } < \infty$ 
B)  $\mathrm { x } = \frac { \mathrm { t } } { 4 } , \mathrm { y } = \mathrm { t } - \frac { 5 } { 4 } ; 0 \leq \mathrm { t } < \infty$ 
C)  $x = t , y = 4 t - 5 ; 0 \leq t < \infty$ 
D)  $x = t , y = 4 t ^ { 2 } - 5 ; 0 \leq t < \infty$

Question 3

Identify the equation without applying a rotation of axes.
-$$3 x ^ { 2 } + 8 x y + 2 y ^ { 2 } + 3 x + 2 y + 10 = 0$$

Accepted Answer

A)  parabola 
B)  hyperbola 
C)  ellipse 
D)  not a conic 
A)  parabola 
B)  hyperbola 
C)  ellipse 
D)  not a conic

Question 4

Find an equation for the ellipse described.
-Center $( 0,0 )$; major axis vertical with length 14 ; length of minor axis is 8

Accepted Answer

A)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 25 } = 1$ 
B)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 196 } = 1$ 
D)  $\frac { x ^ { 2 } } { 10 } + \frac { y ^ { 2 } } { 49 } = 1$ 
A)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 25 } = 1$ 
B)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 196 } = 1$ 
D)  $\frac { x ^ { 2 } } { 10 } + \frac { y ^ { 2 } } { 49 } = 1$

Question 5

Graph the curve whose parametric equations are given.
-$x=2 \tan t, y=4 \sec t ; 0 \leq t \leq 2 \pi$

Accepted Answer

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

Question 6

Find the center, foci, and vertices of the ellipse.
-$$16 ( x + 2 ) ^ { 2 } + 9 ( y - 1 ) ^ { 2 } = 144$$

Accepted Answer

A)  center at $ (-1,1) $
foci at $ (-1,1-\sqrt{7}),(-1,1+\sqrt{7}) $
vertices at $ (-1,5),(-1,-3) $ 
B) center at $ (1,-2) $
foci at $ (1,-2-\sqrt{7}),(1,-2+\sqrt{7}) $
vertices at $ (1,5),(1,-3) $ 
C)  center at $ (2,1) $
foci at $ (2,1-\sqrt{7}),(2,1+\sqrt{7}) $
vertices at $ (2,5),(2,-3) $ 
D)  center at $ (-2,1) $
foci at $ (-2,1-\sqrt{7}),(-2,1+\sqrt{7}) $
vertices at $ (-2,5),(-2,-3) $ 
A)  center at $ (-1,1) $
foci at $ (-1,1-\sqrt{7}),(-1,1+\sqrt{7}) $
vertices at $ (-1,5),(-1,-3) $ 
B) center at $ (1,-2) $
foci at $ (1,-2-\sqrt{7}),(1,-2+\sqrt{7}) $
vertices at $ (1,5),(1,-3) $ 
C)  center at $ (2,1) $
foci at $ (2,1-\sqrt{7}),(2,1+\sqrt{7}) $
vertices at $ (2,5),(2,-3) $ 
D)  center at $ (-2,1) $
foci at $ (-2,1-\sqrt{7}),(-2,1+\sqrt{7}) $
vertices at $ (-2,5),(-2,-3) $

Question 7

Graph the hyperbola.
-$25 x^{2}=9 y^{2}+225$

Accepted Answer

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

Question 8

Identify the equation without completing the square.
-$$2 x ^ { 2 } - 3 y ^ { 2 } + 3 x + 2 y + 2 = 0$$

Accepted Answer

A)  hyperbola 
B)  ellipse 
C)  parabola 
D)  not a conic 
A)  hyperbola 
B)  ellipse 
C)  parabola 
D)  not a conic

Question 9

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation.
-$$5 x ^ { 2 } - 6 x y + 5 y ^ { 2 } - 8 = 0$$

Accepted Answer

A) 
$$
\begin{array}{l}
\theta=45^{\circ} \
y^{2}=-4 x^{\prime}
\end{array}
$$
parabola
vertex at $ (0,0) $
focus at $ (-1,0) $ 
B)  
$$
\theta=45^{\circ}
$$
$$
\frac{x^{\prime 2}}{4}-y^{\prime 2}=1
$$
hyperbola
center at $ (0,0) $
transverse axis is the $ x^{\prime} $-axis
vertices at $ (\pm 2,0) $ 
C) 
$\begin{array}{l}
\theta=45^{\circ} \
x^{\prime 2}=-4 y^{\prime} \
\text { parabola } \
\text { vertex at }(0,0) \
\text { focus at }(0,-1)
\end{array}$ 
D)  
$$
\begin{array}{l}
\theta=45^{\circ} \
\frac{x^{\prime 2}}{4}+y^{\prime 2}=1
\end{array}
$$
ellipse
center at $ (0,0) $
major axis is the $ x^{\prime} $-axis
vertices at $ (\pm 2,0) $ 
A) 
$$
\begin{array}{l}
\theta=45^{\circ} \
y^{2}=-4 x^{\prime}
\end{array}
$$
parabola
vertex at $ (0,0) $
focus at $ (-1,0) $ 
B)  
$$
\theta=45^{\circ}
$$
$$
\frac{x^{\prime 2}}{4}-y^{\prime 2}=1
$$
hyperbola
center at $ (0,0) $
transverse axis is the $ x^{\prime} $-axis
vertices at $ (\pm 2,0) $ 
C) 
$\begin{array}{l}
\theta=45^{\circ} \
x^{\prime 2}=-4 y^{\prime} \
\text { parabola } \
\text { vertex at }(0,0) \
\text { focus at }(0,-1)
\end{array}$ 
D)  
$$
\begin{array}{l}
\theta=45^{\circ} \
\frac{x^{\prime 2}}{4}+y^{\prime 2}=1
\end{array}
$$
ellipse
center at $ (0,0) $
major axis is the $ x^{\prime} $-axis
vertices at $ (\pm 2,0) $

Question 10

Find a rectangular equation for the plane curve defined by the parametric equations.
-$$x = 3 \tan t , y = 2 \sec t ; 0 \leq t \leq 2 \pi$$

Accepted Answer

A)  $y = x ^ { 2 } - 9$; for $x$ in $- 3 \leq x \leq 3$ 
B)  $y = 3 \sqrt { 1 + \frac { x ^ { 2 } } { 25 } }$; for $x$ in $- \infty < x < \infty$ 
C)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$; for $x$ in $- \infty < x < \infty$ 
D)  $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 25 } = 1$; for $x$ in $- \infty < x < \infty$ 
A)  $y = x ^ { 2 } - 9$; for $x$ in $- 3 \leq x \leq 3$ 
B)  $y = 3 \sqrt { 1 + \frac { x ^ { 2 } } { 25 } }$; for $x$ in $- \infty < x < \infty$ 
C)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$; for $x$ in $- \infty < x < \infty$ 
D)  $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 25 } = 1$; for $x$ in $- \infty < x < \infty$

Question 11

Graph the ellipse and locate the foci.
-$$\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$$

Accepted Answer

A)  foci at $( \sqrt { 21 } , 0 )$ and $( - \sqrt { 21 } , 0 )$
  
B)  foci at $( 2 \sqrt { 5 } , 0 )$ and $( - 2 \sqrt { 5 } , 0 )$
  
C)  foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$
  
D)  foci at $( 0,2 \sqrt { 3 } )$ and $( 0 , - 2 \sqrt { 3 } )$
  
A)  foci at $( \sqrt { 21 } , 0 )$ and $( - \sqrt { 21 } , 0 )$
  
B)  foci at $( 2 \sqrt { 5 } , 0 )$ and $( - 2 \sqrt { 5 } , 0 )$
  
C)  foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$
  
D)  foci at $( 0,2 \sqrt { 3 } )$ and $( 0 , - 2 \sqrt { 3 } )$

Question 12

Graph the equation.
-$4(x-1)^{2}+9(y+2)^{2}=36$

Accepted Answer

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

Question 13

Identify the equation without completing the square.
-$$y ^ { 2 } - 4 x ^ { 2 } + 8 x + 4 y + 3 = 0$$

Accepted Answer

A)  parabola 
B)  ellipse 
C)  hyperbola 
D)  not a conic 
A)  parabola 
B)  ellipse 
C)  hyperbola 
D)  not a conic

Question 14

Find an equation for the parabola described.
-Vertex at $( 7,8 )$; focus at $( 3,8 )$

Accepted Answer

A)  $( y - 8 ) ^ { 2 } = - 16 ( x - 7 )$ 
B)  $( y - 8 ) ^ { 2 } = 16 ( x - 7 )$ 
C)  $( x - 8 ) ^ { 2 } = 20 ( y - 8 )$ 
D)  $( x - 8 ) ^ { 2 } = - 20 ( y - 8 )$ 
A)  $( y - 8 ) ^ { 2 } = - 16 ( x - 7 )$ 
B)  $( y - 8 ) ^ { 2 } = 16 ( x - 7 )$ 
C)  $( x - 8 ) ^ { 2 } = 20 ( y - 8 )$ 
D)  $( x - 8 ) ^ { 2 } = - 20 ( y - 8 )$

Question 15

Find the center, foci, and vertices of the ellipse.
-$$9 x ^ { 2 } + 4 y ^ { 2 } = 36$$

Accepted Answer

A)  center at $ (0,0) $
foci at $ (0,3) $ and $ (2,0) $
vertices at $ (0,9) $ and $ (4,0) $ 
B) center at $ (0,0) $
foci at $ (0,-\sqrt{5}) $ and $ (0, \sqrt{5}) $
vertices at $ (0,-3),(0,3) $ 
C)  center at $ (0,0) $
foci at $ (0,-3) $ and $ (0,3) $
vertices at $ (0,-9),(0,9) $ 
D)  center at $ (0,0) $
foci at $ (-\sqrt{5}, 0) $ and $ (\sqrt{5}, 0) $
vertices at $ (-3,0),(3,0) $ 
A)  center at $ (0,0) $
foci at $ (0,3) $ and $ (2,0) $
vertices at $ (0,9) $ and $ (4,0) $ 
B) center at $ (0,0) $
foci at $ (0,-\sqrt{5}) $ and $ (0, \sqrt{5}) $
vertices at $ (0,-3),(0,3) $ 
C)  center at $ (0,0) $
foci at $ (0,-3) $ and $ (0,3) $
vertices at $ (0,-9),(0,9) $ 
D)  center at $ (0,0) $
foci at $ (-\sqrt{5}, 0) $ and $ (\sqrt{5}, 0) $
vertices at $ (-3,0),(3,0) $

Question 16

Write the word or phrase that best completes each statement or answers the question.
-A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the
surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 8 feet across at
its opening and is 2 feet deep at its center, at what position should the receiver be placed?

Accepted Answer

The receiver should

Question 17

Solve.
-A baseball player hit a baseball with an initial speed of 160 feet per second at an angle of $40 ^ { \circ }$ to the horizontal. The ball was hit at a height of 4 feet off the ground. 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 distance the ball traveled?

Accepted Answer

A)  $x = 114.9 t$ and $y = - 16 t ^ { 2 } + 96.45 t + 3$
$6.059 \mathrm { sec } , 3.014 \mathrm { sec }$,
$1171.774$ feet 
B)  $x = 114.9 t$ and $y = - 16 t ^ { 2 } + 96.45 t + 3$
$5.997 \mathrm { sec } , 3.014 \mathrm { sec }$,
$689.055$ feet 
C)  $x = 122.56 t$ and $y = - 16 t ^ { 2 } + 102.88 t + 4$
$6.469 \mathrm { sec } , 3.215 \mathrm { sec }$
$12.937 \mathrm { sec } , 3.215 \mathrm { sec }$ 
D)  $x = 122.56 t$ and $y = - 16 t ^ { 2 } + 102.88 t + 4$
$792.841$ feet
$1,585.559$ feet 
A)  $x = 114.9 t$ and $y = - 16 t ^ { 2 } + 96.45 t + 3$
$6.059 \mathrm { sec } , 3.014 \mathrm { sec }$,
$1171.774$ feet 
B)  $x = 114.9 t$ and $y = - 16 t ^ { 2 } + 96.45 t + 3$
$5.997 \mathrm { sec } , 3.014 \mathrm { sec }$,
$689.055$ feet 
C)  $x = 122.56 t$ and $y = - 16 t ^ { 2 } + 102.88 t + 4$
$6.469 \mathrm { sec } , 3.215 \mathrm { sec }$
$12.937 \mathrm { sec } , 3.215 \mathrm { sec }$ 
D)  $x = 122.56 t$ and $y = - 16 t ^ { 2 } + 102.88 t + 4$
$792.841$ feet
$1,585.559$ feet

Question 18

Choose the one alternative that best completes the statement or answers the question.
Use a graphing utility to graph the curve defined by the given parametric equations.
-$x=t+2, y=3 t-1 ; 0 \leq t \leq 3$

Accepted Answer

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

Question 19

Find the center, foci, and vertices of the ellipse.
-$$\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$$

Accepted Answer

A)  center at $ (1,-2) $
foci at $ (1+3 \sqrt{3}, 1),(1-3 \sqrt{3}, 1) $
vertices at $ (6,-2),(-6,-2) $ 
B) $\begin{array}{l}
\text { center at }(-2,1) \
\text { foci at }(-2+3 \sqrt{3}, 1),(-2-3 \sqrt{3}, 1) \
\text { vertices at }(-5,-2),(7,-2)
\end{array}$ 
C) center at $ (1,-2) $
foci at $ (-3 \sqrt{3},-2),(3 \sqrt{3},-2) $
vertices at $ (6,-2),(-6,-2) $ 
D)  center at $ (1,-2) $
foci at $ (1+3 \sqrt{3},-2),(1-3 \sqrt{3},-2) $
vertices at $ (-5,-2),(7,-2) $ 
A)  center at $ (1,-2) $
foci at $ (1+3 \sqrt{3}, 1),(1-3 \sqrt{3}, 1) $
vertices at $ (6,-2),(-6,-2) $ 
B) $\begin{array}{l}
\text { center at }(-2,1) \
\text { foci at }(-2+3 \sqrt{3}, 1),(-2-3 \sqrt{3}, 1) \
\text { vertices at }(-5,-2),(7,-2)
\end{array}$ 
C) center at $ (1,-2) $
foci at $ (-3 \sqrt{3},-2),(3 \sqrt{3},-2) $
vertices at $ (6,-2),(-6,-2) $ 
D)  center at $ (1,-2) $
foci at $ (1+3 \sqrt{3},-2),(1-3 \sqrt{3},-2) $
vertices at $ (-5,-2),(7,-2) $

Question 20

Graph the equation.
-$y^{2}=16 x$

Accepted Answer

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

A) $y = 20 x ^ { 2 }$ B) $x = 20 y ^ { 2 }$ C) $x ^ { 2 } = 20 y$ D) $y ^ { 2 } = 20 x$ -Vertex at (0, 0); axis of symmetry the x-axis; containing the point (9, 5)

Find parametric equations for the rectangular equation. - $y=4 x-5$

Identify the equation without applying a rotation of axes. - $3 x ^ { 2 } + 8 x y + 2 y ^ { 2 } + 3 x + 2 y + 10 = 0$

Find an equation for the ellipse described. -Center $( 0,0 )$ ; major axis vertical with length 14 ; length of minor axis is 8

Graph the curve whose parametric equations are given. - $x=2 \tan t, y=4 \sec t ; 0 \leq t \leq 2 \pi$ $Graph the curve whose parametric equations are given. - x=2 \tan t, y=4 \sec t ; 0 \leq t \leq 2 \pi$

Find the center, foci, and vertices of the ellipse. - $16 ( x + 2 ) ^ { 2 } + 9 ( y - 1 ) ^ { 2 } = 144$

Graph the hyperbola. - $25 x^{2}=9 y^{2}+225$ $Graph the hyperbola. - 25 x^{2}=9 y^{2}+225$

Identify the equation without completing the square. - $2 x ^ { 2 } - 3 y ^ { 2 } + 3 x + 2 y + 2 = 0$

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. - $5 x ^ { 2 } - 6 x y + 5 y ^ { 2 } - 8 = 0$

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = 3 \tan t , y = 2 \sec t ; 0 \leq t \leq 2 \pi$

Graph the ellipse and locate the foci. - $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$ $Graph the ellipse and locate the foci. - \frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$

Graph the equation. - $4(x-1)^{2}+9(y+2)^{2}=36$ $Graph the equation. - 4(x-1)^{2}+9(y+2)^{2}=36$

Identify the equation without completing the square. - $y ^ { 2 } - 4 x ^ { 2 } + 8 x + 4 y + 3 = 0$

Find an equation for the parabola described. -Vertex at $( 7,8 )$ ; focus at $( 3,8 )$

Find the center, foci, and vertices of the ellipse. - $9 x ^ { 2 } + 4 y ^ { 2 } = 36$

Find the center, foci, and vertices of the ellipse. - $\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$

Graph the equation. - $y^{2}=16 x$ $Graph the equation. - y^{2}=16 x$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 9: Analytic Geometry

A) y=20x2y = 20 x ^ { 2 }y=20x2 B) x=20y2x = 20 y ^ { 2 }x=20y2 C) x2=20yx ^ { 2 } = 20 yx2=20y D) y2=20xy ^ { 2 } = 20 xy2=20x -Vertex at (0, 0); axis of symmetry the x-axis; containing the point (9, 5)

Find parametric equations for the rectangular equation. - y=4x−5y=4 x-5y=4x−5

Identify the equation without applying a rotation of axes. - 3x2+8xy+2y2+3x+2y+10=03 x ^ { 2 } + 8 x y + 2 y ^ { 2 } + 3 x + 2 y + 10 = 03x2+8xy+2y2+3x+2y+10=0

Find an equation for the ellipse described. -Center (0,0)( 0,0 )(0,0) ; major axis vertical with length 14 ; length of minor axis is 8

Graph the curve whose parametric equations are given. - x=2tan⁡t,y=4sec⁡t;0≤t≤2πx=2 \tan t, y=4 \sec t ; 0 \leq t \leq 2 \pix=2tant,y=4sect;0≤t≤2π

Find the center, foci, and vertices of the ellipse. - 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

Graph the hyperbola. - 25x2=9y2+22525 x^{2}=9 y^{2}+22525x2=9y2+225

Identify the equation without completing the square. - 2x2−3y2+3x+2y+2=02 x ^ { 2 } - 3 y ^ { 2 } + 3 x + 2 y + 2 = 02x2−3y2+3x+2y+2=0

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. - 5x2−6xy+5y2−8=05 x ^ { 2 } - 6 x y + 5 y ^ { 2 } - 8 = 05x2−6xy+5y2−8=0

Find a rectangular equation for the plane curve defined by the parametric equations. - x=3tan⁡t,y=2sec⁡t;0≤t≤2πx = 3 \tan t , y = 2 \sec t ; 0 \leq t \leq 2 \pix=3tant,y=2sect;0≤t≤2π

Graph the ellipse and locate the foci. - x216+y29=1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 116x2​+9y2​=1

Graph the equation. - 4(x−1)2+9(y+2)2=364(x-1)^{2}+9(y+2)^{2}=364(x−1)2+9(y+2)2=36

Identify the equation without completing the square. - y2−4x2+8x+4y+3=0y ^ { 2 } - 4 x ^ { 2 } + 8 x + 4 y + 3 = 0y2−4x2+8x+4y+3=0

Find an equation for the parabola described. -Vertex at (7,8)( 7,8 )(7,8) ; focus at (3,8)( 3,8 )(3,8)

Find the center, foci, and vertices of the ellipse. - 9x2+4y2=369 x ^ { 2 } + 4 y ^ { 2 } = 369x2+4y2=36

Choose the one alternative that best completes the statement or answers the question. Use a graphing utility to graph the curve defined by the given parametric equations. - x=t+2,y=3t−1;0≤t≤3x=t+2, y=3 t-1 ; 0 \leq t \leq 3x=t+2,y=3t−1;0≤t≤3

Find the center, foci, and vertices of the ellipse. - (x−1)236+(y+2)29=1\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 136(x−1)2​+9(y+2)2​=1

Graph the equation. - y2=16xy^{2}=16 xy2=16x

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

A) $y = 20 x ^ { 2 }$ B) $x = 20 y ^ { 2 }$ C) $x ^ { 2 } = 20 y$ D) $y ^ { 2 } = 20 x$ -Vertex at (0, 0); axis of symmetry the x-axis; containing the point (9, 5)

Find parametric equations for the rectangular equation. - $y=4 x-5$

Identify the equation without applying a rotation of axes. - $3 x ^ { 2 } + 8 x y + 2 y ^ { 2 } + 3 x + 2 y + 10 = 0$

Find an equation for the ellipse described. -Center $( 0,0 )$ ; major axis vertical with length 14 ; length of minor axis is 8

Graph the curve whose parametric equations are given. - $x=2 \tan t, y=4 \sec t ; 0 \leq t \leq 2 \pi$ $Graph the curve whose parametric equations are given. - x=2 \tan t, y=4 \sec t ; 0 \leq t \leq 2 \pi$

Find the center, foci, and vertices of the ellipse. - $16 ( x + 2 ) ^ { 2 } + 9 ( y - 1 ) ^ { 2 } = 144$

Graph the hyperbola. - $25 x^{2}=9 y^{2}+225$ $Graph the hyperbola. - 25 x^{2}=9 y^{2}+225$

Identify the equation without completing the square. - $2 x ^ { 2 } - 3 y ^ { 2 } + 3 x + 2 y + 2 = 0$

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. - $5 x ^ { 2 } - 6 x y + 5 y ^ { 2 } - 8 = 0$

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = 3 \tan t , y = 2 \sec t ; 0 \leq t \leq 2 \pi$

Graph the ellipse and locate the foci. - $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$ $Graph the ellipse and locate the foci. - \frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$

Graph the equation. - $4(x-1)^{2}+9(y+2)^{2}=36$ $Graph the equation. - 4(x-1)^{2}+9(y+2)^{2}=36$

Identify the equation without completing the square. - $y ^ { 2 } - 4 x ^ { 2 } + 8 x + 4 y + 3 = 0$

Find an equation for the parabola described. -Vertex at $( 7,8 )$ ; focus at $( 3,8 )$

Find the center, foci, and vertices of the ellipse. - $9 x ^ { 2 } + 4 y ^ { 2 } = 36$

Find the center, foci, and vertices of the ellipse. - $\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$

Graph the equation. - $y^{2}=16 x$ $Graph the equation. - y^{2}=16 x$