Question 1

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

Accepted Answer

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

Question 2

Solve.
-Ron throws a ball straight up with an initial speed of 70 feet per second from a height of 3 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)  $x = 0$ and $y = - 16 t ^ { 2 } + 40 t + 6$
$5.284 \mathrm { sec } , 1.25 \mathrm { sec }$
25 feet 
B)  $x = 0$ and $y = - 16 t ^ { 2 } + 40 t + 6$
$2.34 \mathrm { sec } , 1.25 \mathrm { sec }$,
$5.99$ feet 
C) $\begin{array}{l}
x=0 \text { and } y=-16 t^{2}+40 t+6 \
4.679 \mathrm{sec}, 1.25 \mathrm{sec} \
181.21 \text { feet }
\end{array}$ 
D)  $x = 0$ and $y = - 16 t ^ { 2 } + 40 t + 6$
$2.642 \mathrm { sec } , 1.25 \mathrm { sec }$
$181.21$ feet
31 feet 
A)  $x = 0$ and $y = - 16 t ^ { 2 } + 40 t + 6$
$5.284 \mathrm { sec } , 1.25 \mathrm { sec }$
25 feet 
B)  $x = 0$ and $y = - 16 t ^ { 2 } + 40 t + 6$
$2.34 \mathrm { sec } , 1.25 \mathrm { sec }$,
$5.99$ feet 
C) $\begin{array}{l}
x=0 \text { and } y=-16 t^{2}+40 t+6 \
4.679 \mathrm{sec}, 1.25 \mathrm{sec} \
181.21 \text { feet }
\end{array}$ 
D)  $x = 0$ and $y = - 16 t ^ { 2 } + 40 t + 6$
$2.642 \mathrm { sec } , 1.25 \mathrm { sec }$
$181.21$ feet
31 feet

Question 3

Identify the equation without applying a rotation of axes.
-$$x ^ { 2 } - 3 x y - 3 y ^ { 2 } - 2 x - 3 y - 5 = 0$$

Accepted Answer

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

Question 4

Find the vertex, focus, and directrix of the parabola. Graph the equation.
-$(y+2)^{2}=8(x+3)$

Accepted Answer

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

Question 5

Graph the equation.
-$y^{2}=-20 x$

Accepted Answer

A) 
  
B)

C) 
  
D) 
  
A) 
  
B)

C) 
  
D)

Question 6

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

Accepted Answer

A)  $y = \frac { 1 } { 3 } x - 1$; for $x$ in $- \infty < x < \infty$ 
B)  $y = x ^ { 2 } + 1$; for $x$ in $- 2 \leq x \leq 2$ 
C)  $y = - 3 x + 1$; for $x$ in $- \infty < x < \infty$ 
D)  $y = \frac { 1 } { 3 } x + 1$; for $x$ in $- 6 \leq x \leq 9$ 
A)  $y = \frac { 1 } { 3 } x - 1$; for $x$ in $- \infty < x < \infty$ 
B)  $y = x ^ { 2 } + 1$; for $x$ in $- 2 \leq x \leq 2$ 
C)  $y = - 3 x + 1$; for $x$ in $- \infty < x < \infty$ 
D)  $y = \frac { 1 } { 3 } x + 1$; for $x$ in $- 6 \leq x \leq 9$

Question 7

Name the conic.
-

Accepted Answer

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

Question 8

Find an equation for the hyperbola described.
-Vertices at $( 0 , \pm 8 )$; asymptotes at $y = \pm \frac { 4 } { 3 } x$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$ 
B)  $\frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 36 } = 1$ 
C)  $\frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 9 } = 1$ 
D)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 64 } = 1$ 
A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$ 
B)  $\frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 36 } = 1$ 
C)  $\frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 9 } = 1$ 
D)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 64 } = 1$

Question 9

Find a rectangular equation for the plane curve defined by the parametric equations.
-$$x = 7 \sin t , y = 7 \cos t ; 0 \leq t \leq 2 \pi$$

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } = 49$; for $x$ in $- 7 \leq x \leq 7$ 
B)  $y = x ^ { 2 } - 9$; for $x$ in $- 2 \leq x \leq 2$ 
C)  $y = \sqrt { a ^ { 2 } - x ^ { 2 } } = 49$; for $x$ in $- \infty < x < \infty$ 
D)  $\mathrm { y } ^ { 2 } - \mathrm { x } ^ { 2 } = 49$; for $\mathrm { x }$ in $- \infty < \mathrm { x } < \infty$ 
A)  $x ^ { 2 } + y ^ { 2 } = 49$; for $x$ in $- 7 \leq x \leq 7$ 
B)  $y = x ^ { 2 } - 9$; for $x$ in $- 2 \leq x \leq 2$ 
C)  $y = \sqrt { a ^ { 2 } - x ^ { 2 } } = 49$; for $x$ in $- \infty < x < \infty$ 
D)  $\mathrm { y } ^ { 2 } - \mathrm { x } ^ { 2 } = 49$; for $\mathrm { x }$ in $- \infty < \mathrm { x } < \infty$

Question 10

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation.
-$24 x y - 7 y ^ { 2 } + 36 = 0$

Accepted Answer

A) $$
\begin{array}{l}
\theta=36.9^{\circ} \
\frac{y^{\prime 2}}{9}-\frac{x^{\prime 2}}{16}=1
\end{array}
$$
hyperbola
center at $ (0,0) $
transverse axis is the $ y^{\prime} $-axis
vertices at $ (0, \pm 3) $ 
B) $$
\begin{array}{l}
\theta=36.9^{\circ} \
\frac{4 y^{\prime 2}}{9}-\frac{x^{\prime 2}}{4}=1
\end{array}
$$
hyperbola
center at $ (0,0) $
transverse axis is the $ y^{\prime} $-axis
vertices at $ \left(0, \pm \frac{3}{2}\right) $ 
C)  $$
\begin{array}{l}
\theta=36.9^{\circ} \
\frac{y^{\prime 2}}{4}-\frac{4 x^{2}}{9}=1
\end{array}
$$
hyperbola
center at $ (0,0) $
transverse axis is the $ y^{\prime} $-axis
vertices at $ (0, \pm 2) $ 
D) $$
\begin{array}{l}
\theta=53.1^{\circ} \
\frac{y^{\prime 2}}{4}-\frac{4 x^{\prime 2}}{9}=1
\end{array}
$$
hyperbola
center at $ (0,0) $
transverse axis is the $ y^{\prime} $-axis
vertices at $ (0, \pm 2) $ 
A) $$
\begin{array}{l}
\theta=36.9^{\circ} \
\frac{y^{\prime 2}}{9}-\frac{x^{\prime 2}}{16}=1
\end{array}
$$
hyperbola
center at $ (0,0) $
transverse axis is the $ y^{\prime} $-axis
vertices at $ (0, \pm 3) $ 
B) $$
\begin{array}{l}
\theta=36.9^{\circ} \
\frac{4 y^{\prime 2}}{9}-\frac{x^{\prime 2}}{4}=1
\end{array}
$$
hyperbola
center at $ (0,0) $
transverse axis is the $ y^{\prime} $-axis
vertices at $ \left(0, \pm \frac{3}{2}\right) $ 
C)  $$
\begin{array}{l}
\theta=36.9^{\circ} \
\frac{y^{\prime 2}}{4}-\frac{4 x^{2}}{9}=1
\end{array}
$$
hyperbola
center at $ (0,0) $
transverse axis is the $ y^{\prime} $-axis
vertices at $ (0, \pm 2) $ 
D) $$
\begin{array}{l}
\theta=53.1^{\circ} \
\frac{y^{\prime 2}}{4}-\frac{4 x^{\prime 2}}{9}=1
\end{array}
$$
hyperbola
center at $ (0,0) $
transverse axis is the $ y^{\prime} $-axis
vertices at $ (0, \pm 2) $

Question 11

Graph the ellipse and locate the foci.
-$4 x^{2}+16 y^{2}=64$

Accepted Answer

A)  foci at $( 5,0 )$ and $( - 5,0 )$
  
B)  foci at $( \sqrt { 7 } , 0 )$ and $( - \sqrt { 7 } , 0 )$
  
C)  foci at $( 4,0 )$ and $( - 4,0 )$
  
D)  foci at $( 0 , \sqrt { 7 } )$ and $( 0 , - \sqrt { 7 } )$
  
A)  foci at $( 5,0 )$ and $( - 5,0 )$
  
B)  foci at $( \sqrt { 7 } , 0 )$ and $( - \sqrt { 7 } , 0 )$
  
C)  foci at $( 4,0 )$ and $( - 4,0 )$
  
D)  foci at $( 0 , \sqrt { 7 } )$ and $( 0 , - \sqrt { 7 } )$

Question 12

Graph the hyperbola.
-$36 x^{2}-4 y^{2}=144$

Accepted Answer

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

Question 13

Find an equation for the hyperbola described.
-Vertices at $( \pm 2,0 )$; foci at $( \pm 11,0 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 117 } - \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x ^ { 2 } } { 121 } - \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 121 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 117 } = 1$ 
A)  $\frac { x ^ { 2 } } { 117 } - \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x ^ { 2 } } { 121 } - \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 121 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 117 } = 1$

Question 14

Find an equation for the ellipse described.
-Foci at $( \pm 2,0 ) ; \quad x$-intercepts are $\pm 7$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 45 } + \frac { y ^ { 2 } } { 49 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 45 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 45 } = 1$ 
A)  $\frac { x ^ { 2 } } { 45 } + \frac { y ^ { 2 } } { 49 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 45 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 45 } = 1$

Question 15

Graph the hyperbola.
-$(x-2)^{2}-4(y-2)^{2}=4$

Accepted Answer

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

Question 16

Name the conic.
-

Accepted Answer

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

Question 17

Identify the equation without applying a rotation of axes.
-$$x ^ { 2 } + 8 x y + 16 y ^ { 2 } - 2 x + 4 y - 3 = 0$$

Accepted Answer

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

Question 18

Find an equation for the ellipse described.
-Foci at $( 0 , \pm 5 ) ; \quad y$-intercepts are $\pm 8$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 39 } = 1$ 
C)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 39 } = 1$ 
D)  $\frac { x ^ { 2 } } { 39 } + \frac { y ^ { 2 } } { 64 } = 1$ 
A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 39 } = 1$ 
C)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 39 } = 1$ 
D)  $\frac { x ^ { 2 } } { 39 } + \frac { y ^ { 2 } } { 64 } = 1$

Question 19

Find an equation for the parabola described.
-Vertex at $( 7 , - 9 ) ;$ focus at $( 3 , - 9 )$

Accepted Answer

A)  $( x + 8 ) ^ { 2 } = - 4 ( y - 4 )$ 
B)  $( x + 8 ) ^ { 2 } = 4 ( y - 4 )$ 
C)  $( y + 4 ) ^ { 2 } = - 12 ( x - 8 )$ 
D)  $( y + 9 ) ^ { 2 } = 16 ( x - 7 )$ 
A)  $( x + 8 ) ^ { 2 } = - 4 ( y - 4 )$ 
B)  $( x + 8 ) ^ { 2 } = 4 ( y - 4 )$ 
C)  $( y + 4 ) ^ { 2 } = - 12 ( x - 8 )$ 
D)  $( y + 9 ) ^ { 2 } = 16 ( x - 7 )$

Question 20

Solve the problem.
-An experimental model for a suspension bridge is built in the shape of a parabolic arch. 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 are both 12.25 inches tall and stand 70 inches apart. Find the vertical distance from the
Roadway to the cable at a point on the road 14 inches from the lowest point of the cable.

Accepted Answer

A)  2.16 in. 
B)  1.76 in. 
C)  7.84 in. 
D)  1.96 in. 
A)  2.16 in. 
B)  1.76 in. 
C)  7.84 in. 
D)  1.96 in.

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

Identify the equation without applying a rotation of axes. - $x ^ { 2 } - 3 x y - 3 y ^ { 2 } - 2 x - 3 y - 5 = 0$

Find the vertex, focus, and directrix of the parabola. Graph the equation. - $(y+2)^{2}=8(x+3)$ $Find the vertex, focus, and directrix of the parabola. Graph the equation. - (y+2)^{2}=8(x+3)$

Graph the equation. - $y^{2}=-20 x$ $Graph the equation. - y^{2}=-20 x$

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

Name the conic. -

Find an equation for the hyperbola described. -Vertices at $( 0 , \pm 8 )$ ; asymptotes at $y = \pm \frac { 4 } { 3 } x$

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = 7 \sin t , y = 7 \cos t ; 0 \leq t \leq 2 \pi$

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. - $24 x y - 7 y ^ { 2 } + 36 = 0$

Graph the ellipse and locate the foci. - $4 x^{2}+16 y^{2}=64$ $Graph the ellipse and locate the foci. - 4 x^{2}+16 y^{2}=64$

Graph the hyperbola. - $36 x^{2}-4 y^{2}=144$ $Graph the hyperbola. - 36 x^{2}-4 y^{2}=144$

Find an equation for the hyperbola described. -Vertices at $( \pm 2,0 )$ ; foci at $( \pm 11,0 )$

Find an equation for the ellipse described. -Foci at $( \pm 2,0 ) ; \quad x$ -intercepts are $\pm 7$

Graph the hyperbola. - $(x-2)^{2}-4(y-2)^{2}=4$ $Graph the hyperbola. - (x-2)^{2}-4(y-2)^{2}=4$

Name the conic. -

Identify the equation without applying a rotation of axes. - $x ^ { 2 } + 8 x y + 16 y ^ { 2 } - 2 x + 4 y - 3 = 0$

Find an equation for the ellipse described. -Foci at $( 0 , \pm 5 ) ; \quad y$ -intercepts are $\pm 8$

Find an equation for the parabola described. -Vertex at $( 7 , - 9 ) ;$ focus at $( 3 , - 9 )$

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

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

Identify the equation without applying a rotation of axes. - x2−3xy−3y2−2x−3y−5=0x ^ { 2 } - 3 x y - 3 y ^ { 2 } - 2 x - 3 y - 5 = 0x2−3xy−3y2−2x−3y−5=0

Find the vertex, focus, and directrix of the parabola. Graph the equation. - (y+2)2=8(x+3)(y+2)^{2}=8(x+3)(y+2)2=8(x+3)

Graph the equation. - y2=−20xy^{2}=-20 xy2=−20x

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

Name the conic. -

Find an equation for the hyperbola described. -Vertices at (0,±8)( 0 , \pm 8 )(0,±8) ; asymptotes at y=±43xy = \pm \frac { 4 } { 3 } xy=±34​x

Find a rectangular equation for the plane curve defined by the parametric equations. - x=7sin⁡t,y=7cos⁡t;0≤t≤2πx = 7 \sin t , y = 7 \cos t ; 0 \leq t \leq 2 \pix=7sint,y=7cost;0≤t≤2π

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. - 24xy−7y2+36=024 x y - 7 y ^ { 2 } + 36 = 024xy−7y2+36=0

Graph the ellipse and locate the foci. - 4x2+16y2=644 x^{2}+16 y^{2}=644x2+16y2=64

Graph the hyperbola. - 36x2−4y2=14436 x^{2}-4 y^{2}=14436x2−4y2=144

Find an equation for the hyperbola described. -Vertices at (±2,0)( \pm 2,0 )(±2,0) ; foci at (±11,0)( \pm 11,0 )(±11,0)

Find an equation for the ellipse described. -Foci at (±2,0);x( \pm 2,0 ) ; \quad x(±2,0);x -intercepts are ±7\pm 7±7

Graph the hyperbola. - (x−2)2−4(y−2)2=4(x-2)^{2}-4(y-2)^{2}=4(x−2)2−4(y−2)2=4

Name the conic. -

Identify the equation without applying a rotation of axes. - x2+8xy+16y2−2x+4y−3=0x ^ { 2 } + 8 x y + 16 y ^ { 2 } - 2 x + 4 y - 3 = 0x2+8xy+16y2−2x+4y−3=0

Find an equation for the ellipse described. -Foci at (0,±5);y( 0 , \pm 5 ) ; \quad y(0,±5);y -intercepts are ±8\pm 8±8

Find an equation for the parabola described. -Vertex at (7,−9);( 7 , - 9 ) ;(7,−9); focus at (3,−9)( 3 , - 9 )(3,−9)

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

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

Identify the equation without applying a rotation of axes. - $x ^ { 2 } - 3 x y - 3 y ^ { 2 } - 2 x - 3 y - 5 = 0$

Find the vertex, focus, and directrix of the parabola. Graph the equation. - $(y+2)^{2}=8(x+3)$ $Find the vertex, focus, and directrix of the parabola. Graph the equation. - (y+2)^{2}=8(x+3)$

Graph the equation. - $y^{2}=-20 x$ $Graph the equation. - y^{2}=-20 x$

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

Find an equation for the hyperbola described. -Vertices at $( 0 , \pm 8 )$ ; asymptotes at $y = \pm \frac { 4 } { 3 } x$

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = 7 \sin t , y = 7 \cos t ; 0 \leq t \leq 2 \pi$

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. - $24 x y - 7 y ^ { 2 } + 36 = 0$

Graph the ellipse and locate the foci. - $4 x^{2}+16 y^{2}=64$ $Graph the ellipse and locate the foci. - 4 x^{2}+16 y^{2}=64$

Graph the hyperbola. - $36 x^{2}-4 y^{2}=144$ $Graph the hyperbola. - 36 x^{2}-4 y^{2}=144$

Find an equation for the hyperbola described. -Vertices at $( \pm 2,0 )$ ; foci at $( \pm 11,0 )$

Find an equation for the ellipse described. -Foci at $( \pm 2,0 ) ; \quad x$ -intercepts are $\pm 7$

Graph the hyperbola. - $(x-2)^{2}-4(y-2)^{2}=4$ $Graph the hyperbola. - (x-2)^{2}-4(y-2)^{2}=4$

Identify the equation without applying a rotation of axes. - $x ^ { 2 } + 8 x y + 16 y ^ { 2 } - 2 x + 4 y - 3 = 0$

Find an equation for the ellipse described. -Foci at $( 0 , \pm 5 ) ; \quad y$ -intercepts are $\pm 8$

Find an equation for the parabola described. -Vertex at $( 7 , - 9 ) ;$ focus at $( 3 , - 9 )$