Question 1

Find an equation for the ellipse described.
-Center at $( 0,0 )$; focus at $( - 3,0 )$; vertex at $( 4,0 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 7 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 48 } = 1$ 
A)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 7 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 48 } = 1$

Question 2

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

Accepted Answer

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

Question 3

Solve the problem.
-A bridge is built in the shape of a semielliptical arch. It has a span of 94 feet. The height of the arch 30 feet from the center is to be 6 feet. Find the height of the arch at its center.

Accepted Answer

A)  30.25 ft 
B)  7.79 ft 
C)  6.33 ft 
D)  9.4 ft 
A)  30.25 ft 
B)  7.79 ft 
C)  6.33 ft 
D)  9.4 ft

Question 4

Find the vertex, focus, and directrix of the parabola. Graph the equation.
-$x^{2}-8 x=12 y-76$

Accepted Answer

A) 
vertex: $ (4,5) $
focus: $ (4,2) $
directrix: $ y=8 $
  
B) 
vertex: $ (4,5) $
focus: $ (7,5) $
directrix: $ x=1 $
  
C) 
vertex: $ (4,5) $
focus: $ (1,5) $
directrix: $ x=7 $
  
D) 
vertex: $ (4,5) $
focus: $ (4,8) $
directrix: $ y=2 $

Question 5

Find an equation for the hyperbola described. Graph the equation.
-Center at $( 0,0 ) ;$ vertex at $( 0,3 ) ;$ focus at $( 0 , \sqrt { 13 } )$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$
  
B)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 9 } = 1$
  
C)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$
  
D)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$
  
A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$
  
B)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 9 } = 1$
  
C)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$
  
D)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$

Question 6

Discuss the equation and graph it.
-$r=\frac{4}{2-\sin \theta}$

Accepted Answer

A) directrix perpendicular to polar axis 8 right of pole
center $ \left(-\frac{8}{15}, 0\right) $
$ \operatorname{vertices}\left(\frac{8}{3}, \pi\right),\left(\frac{8}{5}, 0\right) $

B)  directrix parallel to polar axis 8 above pole center $ \left(-\frac{8}{15}, \frac{\pi}{2}\right) $
vertices $ \left(-\frac{8}{5}, \frac{3 \pi}{2}\right),\left(\frac{8}{3}, \frac{3 \pi}{2}\right) $

C) directrix perpendicular to polar axis 8 left of pole
center $ \left(\frac{8}{15}, 0\right) $
vertices $ \left(\frac{8}{5}, \pi\right),\left(\frac{8}{3}, 0\right) $
  
D)  directrix parallel to polar axis 8 below pole center $ \left(\frac{8}{15}, \frac{\pi}{2}\right) $
vertices $ \left(\frac{8}{3}, \frac{\pi}{2}\right),\left(\frac{8}{5}, \frac{3 \pi}{2}\right) $
  
A) directrix perpendicular to polar axis 8 right of pole
center $ \left(-\frac{8}{15}, 0\right) $
$ \operatorname{vertices}\left(\frac{8}{3}, \pi\right),\left(\frac{8}{5}, 0\right) $

B)  directrix parallel to polar axis 8 above pole center $ \left(-\frac{8}{15}, \frac{\pi}{2}\right) $
vertices $ \left(-\frac{8}{5}, \frac{3 \pi}{2}\right),\left(\frac{8}{3}, \frac{3 \pi}{2}\right) $

C) directrix perpendicular to polar axis 8 left of pole
center $ \left(\frac{8}{15}, 0\right) $
vertices $ \left(\frac{8}{5}, \pi\right),\left(\frac{8}{3}, 0\right) $
  
D)  directrix parallel to polar axis 8 below pole center $ \left(\frac{8}{15}, \frac{\pi}{2}\right) $
vertices $ \left(\frac{8}{3}, \frac{\pi}{2}\right),\left(\frac{8}{5}, \frac{3 \pi}{2}\right) $

Question 7

Find an equation of the parabola described.
-Focus at (-3, 0); directrix the line x = 3

Accepted Answer

A)  $y ^ { 2 } = - 12 x$ 
B)  $x ^ { 2 } = - 12 y$ 
C)  $y ^ { 2 } = - 3 x$ 
D)  $y ^ { 2 } = 12 x$ 
A)  $y ^ { 2 } = - 12 x$ 
B)  $x ^ { 2 } = - 12 y$ 
C)  $y ^ { 2 } = - 3 x$ 
D)  $y ^ { 2 } = 12 x$

Question 8

Find the vertex, focus, and directrix of the parabola.
-$x^{2}=-8 y$

Accepted Answer

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

Question 9

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

Accepted Answer

A)  foci at $( \sqrt { 13 } , 0 )$ and $( - \sqrt { 13 } , 0 )$
  
B)  foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$
  
C)  foci at $( 0 , \sqrt { 5 } )$ and $( 0 , - \sqrt { 5 } )$
  
D)  foci at $( \sqrt { 5 } , 0 )$ and $( - \sqrt { 5 } , 0 )$
  
A)  foci at $( \sqrt { 13 } , 0 )$ and $( - \sqrt { 13 } , 0 )$
  
B)  foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$
  
C)  foci at $( 0 , \sqrt { 5 } )$ and $( 0 , - \sqrt { 5 } )$
  
D)  foci at $( \sqrt { 5 } , 0 )$ and $( - \sqrt { 5 } , 0 )$

Question 10

Graph the hyperbola.
-$\frac{y^{2}}{4}-\frac{x^{2}}{16}=1$

Accepted Answer

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

Question 11

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation.
-$x y + 16 = 0$

Accepted Answer

A)  $$
\theta=45^{\circ}
$$
$$
\frac{y^{\prime 2}}{32}+\frac{x^{\prime 2}}{32}=1
$$
ellipse
center at $ (0,0) $
major axis is $ y^{\prime} $-axis
vertices at $ (0, \pm 4 \sqrt{2}) $ 
B)  $$
\theta=45^{\circ}
$$
$$
\frac{y^{\prime 2}}{32}-\frac{x^{\prime 2}}{32}=1
$$
hyperbola
center at $ (0,0) $
transverse axis is $ \mathrm{y}^{\prime} $-axis
vertices at $ (0, \pm 4 \sqrt{2}) $ 
C)  $\begin{array}{l}
\theta=45^{\circ} \
y^{\prime 2}=-32 x^{\prime} \
\text { parabola } \
\text { vertex at }(0,0) \
\text { focus at }(-8,0)
\end{array}$ 
D)  $$
\begin{array}{l}
\theta=36.9^{0} \
\frac{x^{12}}{4}+\frac{y^{\prime 2}}{2}=1
\end{array}
$$
ellipse
center at $ (0,0) $
major axis is the $ x^{\prime} $-axis
vertices at $ (\pm 2,0) $ 
A)  $$
\theta=45^{\circ}
$$
$$
\frac{y^{\prime 2}}{32}+\frac{x^{\prime 2}}{32}=1
$$
ellipse
center at $ (0,0) $
major axis is $ y^{\prime} $-axis
vertices at $ (0, \pm 4 \sqrt{2}) $ 
B)  $$
\theta=45^{\circ}
$$
$$
\frac{y^{\prime 2}}{32}-\frac{x^{\prime 2}}{32}=1
$$
hyperbola
center at $ (0,0) $
transverse axis is $ \mathrm{y}^{\prime} $-axis
vertices at $ (0, \pm 4 \sqrt{2}) $ 
C)  $\begin{array}{l}
\theta=45^{\circ} \
y^{\prime 2}=-32 x^{\prime} \
\text { parabola } \
\text { vertex at }(0,0) \
\text { focus at }(-8,0)
\end{array}$ 
D)  $$
\begin{array}{l}
\theta=36.9^{0} \
\frac{x^{12}}{4}+\frac{y^{\prime 2}}{2}=1
\end{array}
$$
ellipse
center at $ (0,0) $
major axis is the $ x^{\prime} $-axis
vertices at $ (\pm 2,0) $

Question 12

Find a rectangular equation for the plane curve defined by the parametric equations.
-$$x = t ^ { 3 } + 1 , y = t ^ { 3 } - 10 ; - 2 \leq t \leq 2$$

Accepted Answer

A)  $y = x - 11$; for $x$ in $- 7 \leq x \leq 9$ 
B)  $y = - x - 11$; for $x$ in $- 7 \leq x \leq 9$ 
C)  $y = x ^ { 3 }$; for $x$ in $- 3 \leq x \leq 1$ 
D)  $y = - x ^ { 2 }$; for $x$ in $- 4 \leq x \leq 4$ 
A)  $y = x - 11$; for $x$ in $- 7 \leq x \leq 9$ 
B)  $y = - x - 11$; for $x$ in $- 7 \leq x \leq 9$ 
C)  $y = x ^ { 3 }$; for $x$ in $- 3 \leq x \leq 1$ 
D)  $y = - x ^ { 2 }$; for $x$ in $- 4 \leq x \leq 4$

Question 13

Find an equation for the ellipse described.
-Focus at $( 0 , - 4 )$; vertices at $( 0 , \pm 8 )$

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
-$$x ^ { 2 } - 16 y ^ { 2 } + 6 x - 32 y - 23 = 0$$

Accepted Answer

A)  center at $( - 3 , - 1 )$
transverse axis is parallel to $x$-axis
vertices at $( - 7 , - 1 )$ and $( 1 , - 1 )$
foci at $( - 3 - \sqrt { 17 } , - 1 )$ and $( - 3 + \sqrt { 17 } , - 1 )$
asymptotes of $y + 1 = - \frac { 1 } { 4 } ( x + 3 )$ and $y + 1 = \frac { 1 } { 4 } ( x + 3 )$ 
B)  center at $( - 3 , - 1 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices at $( - 3 , - 5 )$ and $( - 3,3 )$
foci at $( - 3 , - 1 - \sqrt { 17 } )$ and $( - 3 , - 1 + \sqrt { 17 } )$
asymptotes of $\mathrm { y } - 1 = - 4 ( \mathrm { x } - 3 )$ and $\mathrm { y } - 1 = 4 ( \mathrm { x } - 3 )$ 
C)  center at $( - 3 , - 1 )$
transverse axis is parallel to $x$-axis
vertices at $( - 4 , - 1 )$ and $( - 2 , - 1 )$
foci at $( - 3 - \sqrt { 17 } , - 1 )$ and $( - 3 + \sqrt { 17 } , - 1 )$
asymptotes of $\mathrm { y } + 1 = - 4 ( \mathrm { x } + 3 )$ and $\mathrm { y } + 1 = 4 ( \mathrm { x } + 3 )$ 
D)  center at $( - 1 , - 3 )$
transverse axis is parallel to $x$-axis
vertices at $( - 5 , - 3 )$ and $( 3 , - 3 )$
foci at $( - 1 - \sqrt { 17 } , - 3 )$ and $( - 1 + \sqrt { 17 } , - 3 )$
asymptotes of $y + 3 = - \frac { 1 } { 4 } ( x + 1 )$ and $y + 3 = \frac { 1 } { 4 } ( x + 1 )$ 
A)  center at $( - 3 , - 1 )$
transverse axis is parallel to $x$-axis
vertices at $( - 7 , - 1 )$ and $( 1 , - 1 )$
foci at $( - 3 - \sqrt { 17 } , - 1 )$ and $( - 3 + \sqrt { 17 } , - 1 )$
asymptotes of $y + 1 = - \frac { 1 } { 4 } ( x + 3 )$ and $y + 1 = \frac { 1 } { 4 } ( x + 3 )$ 
B)  center at $( - 3 , - 1 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices at $( - 3 , - 5 )$ and $( - 3,3 )$
foci at $( - 3 , - 1 - \sqrt { 17 } )$ and $( - 3 , - 1 + \sqrt { 17 } )$
asymptotes of $\mathrm { y } - 1 = - 4 ( \mathrm { x } - 3 )$ and $\mathrm { y } - 1 = 4 ( \mathrm { x } - 3 )$ 
C)  center at $( - 3 , - 1 )$
transverse axis is parallel to $x$-axis
vertices at $( - 4 , - 1 )$ and $( - 2 , - 1 )$
foci at $( - 3 - \sqrt { 17 } , - 1 )$ and $( - 3 + \sqrt { 17 } , - 1 )$
asymptotes of $\mathrm { y } + 1 = - 4 ( \mathrm { x } + 3 )$ and $\mathrm { y } + 1 = 4 ( \mathrm { x } + 3 )$ 
D)  center at $( - 1 , - 3 )$
transverse axis is parallel to $x$-axis
vertices at $( - 5 , - 3 )$ and $( 3 , - 3 )$
foci at $( - 1 - \sqrt { 17 } , - 3 )$ and $( - 1 + \sqrt { 17 } , - 3 )$
asymptotes of $y + 3 = - \frac { 1 } { 4 } ( x + 1 )$ and $y + 3 = \frac { 1 } { 4 } ( x + 1 )$

Question 16

Solve the problem.
-Two recording devices are set 2,800 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)  430.77 feet 
B)  5562.37 feet 
C)  1142.61 feet 
D)  1486.61 feet 
A)  430.77 feet 
B)  5562.37 feet 
C)  1142.61 feet 
D)  1486.61 feet

Question 17

Name the conic.
-

Accepted Answer

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

Question 18

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

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 19

Find the vertex, focus, and directrix of the parabola. Graph the equation.
-$y^{2}+12 y=4 x-16$

Accepted Answer

A)  vertex: $( - 5 , - 6 )$
focus: $( - 4 , - 6 )$
directrix: $x = - 6$
  
B)  vertex: $( - 5 , - 6 )$
focus: $( - 6 , - 6 )$
directrix: $x = - 4$
  
C)  vertex: $( - 5 , - 6 )$
focus: $( - 5 , - 7 )$
directrix: $y = - 5$
  
D)  vertex: $( - 5 , - 6 )$
focus: $( - 5 , - 5 )$
directrix: $y = - 7$
  
A)  vertex: $( - 5 , - 6 )$
focus: $( - 4 , - 6 )$
directrix: $x = - 6$
  
B)  vertex: $( - 5 , - 6 )$
focus: $( - 6 , - 6 )$
directrix: $x = - 4$
  
C)  vertex: $( - 5 , - 6 )$
focus: $( - 5 , - 7 )$
directrix: $y = - 5$
  
D)  vertex: $( - 5 , - 6 )$
focus: $( - 5 , - 5 )$
directrix: $y = - 7$

Question 20

Write the word or phrase that best completes each statement or answers the question.
-A hall 130 feet in length was designed as a whispering gallery. If the ceiling is 25 feet high at the center, how far
from the center are the foci located?

Accepted Answer

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

Find an equation for the ellipse described. -Center at $( 0,0 )$ ; focus at $( - 3,0 )$ ; vertex at $( 4,0 )$

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

Solve the problem. -A bridge is built in the shape of a semielliptical arch. It has a span of 94 feet. The height of the arch 30 feet from the center is to be 6 feet. Find the height of the arch at its center.

Find the vertex, focus, and directrix of the parabola. Graph the equation. - $x^{2}-8 x=12 y-76$ $Find the vertex, focus, and directrix of the parabola. Graph the equation. - x^{2}-8 x=12 y-76$

Find an equation for the hyperbola described. Graph the equation. -Center at $( 0,0 ) ;$ vertex at $( 0,3 ) ;$ focus at $( 0 , \sqrt { 13 } )$ $Find an equation for the hyperbola described. Graph the equation. -Center at ( 0,0 ) ; vertex at ( 0,3 ) ; focus at ( 0 , \sqrt { 13 } )$

Discuss the equation and graph it. - $r=\frac{4}{2-\sin \theta}$ $Discuss the equation and graph it. - r=\frac{4}{2-\sin \theta}$

Find an equation of the parabola described. -Focus at (-3, 0); directrix the line x = 3

Find the vertex, focus, and directrix of the parabola. - $x^{2}=-8 y$ $Find the vertex, focus, and directrix of the parabola. - x^{2}=-8 y$

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

Graph the hyperbola. - $\frac{y^{2}}{4}-\frac{x^{2}}{16}=1$ $Graph the hyperbola. - \frac{y^{2}}{4}-\frac{x^{2}}{16}=1$

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. - $x y + 16 = 0$

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = t ^ { 3 } + 1 , y = t ^ { 3 } - 10 ; - 2 \leq t \leq 2$

Find an equation for the ellipse described. -Focus at $( 0 , - 4 )$ ; vertices at $( 0 , \pm 8 )$

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

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $x ^ { 2 } - 16 y ^ { 2 } + 6 x - 32 y - 23 = 0$

Name the conic. -

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

Find the vertex, focus, and directrix of the parabola. Graph the equation. - $y^{2}+12 y=4 x-16$ $Find the vertex, focus, and directrix of the parabola. Graph the equation. - y^{2}+12 y=4 x-16$

Write the word or phrase that best completes each statement or answers the question. -A hall 130 feet in length was designed as a whispering gallery. If the ceiling is 25 feet high at the center, how far from the center are the foci located?

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

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Exam 9: Analytic Geometry

Find an equation for the ellipse described. -Center at (0,0)( 0,0 )(0,0) ; focus at (−3,0)( - 3,0 )(−3,0) ; vertex at (4,0)( 4,0 )(4,0)

Identify the equation without completing the square. - 2x2−4x+y+2=02 x ^ { 2 } - 4 x + y + 2 = 02x2−4x+y+2=0