Question 1

Find the center, foci, and vertices of the ellipse.
-$$2 x ^ { 2 } + 5 y ^ { 2 } - 12 x + 60 y + 188 = 0$$

Accepted Answer

A)  $\frac { ( x - 3 ) ^ { 2 } } { 2 } + \frac { ( y + 6 ) ^ { 2 } } { 5 } = 1$
center: $( - 3,6 )$; foci: $( - 1.3,6 ) , ( - 4.7,6 )$; vertices: $( - 5.2,6 ) , ( - 0.8,6 )$ 
B)  $\frac { ( x - 3 ) ^ { 2 } } { 5 } + \frac { ( y + 6 ) ^ { 2 } } { 2 } = 1$
center: $( 3 , - 6 )$; foci: $( 4.7 , - 6 ) , ( 1.3 , - 6 )$; vertices: $( 5.2 , - 6 ) , ( 0.8 , - 6 )$ 
C)  $\frac { ( x - 3 ) ^ { 2 } } { 5 } + \frac { ( y + 6 ) ^ { 2 } } { 2 } = 1$
center: $( - 3,6 )$; foci: $( - 1.3,6 ) , ( - 4.7,6 )$; vertices: $( - 5.2,6 ) , ( - 0.8,6 )$ 
D)  $\frac { ( x - 3 ) ^ { 2 } } { 2 } + \frac { ( y + 6 ) ^ { 2 } } { 5 } = 1$
center: $( 3 , - 6 )$; foci: $( 4.7 , - 6 ) , ( 1.3 , - 6 )$; vertices: $( 5.2 , - 6 ) , ( 0.8 , - 6 )$ 
A)  $\frac { ( x - 3 ) ^ { 2 } } { 2 } + \frac { ( y + 6 ) ^ { 2 } } { 5 } = 1$
center: $( - 3,6 )$; foci: $( - 1.3,6 ) , ( - 4.7,6 )$; vertices: $( - 5.2,6 ) , ( - 0.8,6 )$ 
B)  $\frac { ( x - 3 ) ^ { 2 } } { 5 } + \frac { ( y + 6 ) ^ { 2 } } { 2 } = 1$
center: $( 3 , - 6 )$; foci: $( 4.7 , - 6 ) , ( 1.3 , - 6 )$; vertices: $( 5.2 , - 6 ) , ( 0.8 , - 6 )$ 
C)  $\frac { ( x - 3 ) ^ { 2 } } { 5 } + \frac { ( y + 6 ) ^ { 2 } } { 2 } = 1$
center: $( - 3,6 )$; foci: $( - 1.3,6 ) , ( - 4.7,6 )$; vertices: $( - 5.2,6 ) , ( - 0.8,6 )$ 
D)  $\frac { ( x - 3 ) ^ { 2 } } { 2 } + \frac { ( y + 6 ) ^ { 2 } } { 5 } = 1$
center: $( 3 , - 6 )$; foci: $( 4.7 , - 6 ) , ( 1.3 , - 6 )$; vertices: $( 5.2 , - 6 ) , ( 0.8 , - 6 )$ B

Question 2

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

Accepted Answer

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

Question 3

Find the center, foci, and vertices of the ellipse.
-$16 x ^ { 2 } + y ^ { 2 } - 256 x + 1,008 = 0$

Accepted Answer

A)  $( x - 2 ) ^ { 2 } + \frac { y ^ { 2 } } { 64 } = 1$
center: $( 2,0 )$; foci: $( 2,3 \sqrt { 7 } ) , ( 2 , - 3 \sqrt { 7 } )$; vertices: $( 2,8 ) , ( 2 , - 8 )$ 
B)  $( x - 8 ) ^ { 2 } + \frac { y ^ { 2 } } { 4 } = 1$
center: $( 8,0 )$; foci: $( 8 , \sqrt { 3 } ) , ( 8 , - \sqrt { 3 } )$; vertices: $( 8,2 ) , ( 8 , - 2 )$ 
C)  $\frac { x ^ { 2 } } { 64 } + ( y - 2 ) ^ { 2 } = 1$
center: $( 2,0 )$; foci: $( 2,3 \sqrt { 7 } ) , ( 2 , - 3 \sqrt { 7 } )$; vertices: $( 2,8 ) , ( 2 , - 8 )$ 
D)  $\frac { x ^ { 2 } } { 4 } + ( y - 8 ) ^ { 2 } = 1$
center: $( 8,0 )$; foci: $( 8 , \sqrt { 3 } ) , ( 8 , - 3 \sqrt { 7 } )$; vertices: $( 8,2 )$,
$( 8 , - 2 )$ 
A)  $( x - 2 ) ^ { 2 } + \frac { y ^ { 2 } } { 64 } = 1$
center: $( 2,0 )$; foci: $( 2,3 \sqrt { 7 } ) , ( 2 , - 3 \sqrt { 7 } )$; vertices: $( 2,8 ) , ( 2 , - 8 )$ 
B)  $( x - 8 ) ^ { 2 } + \frac { y ^ { 2 } } { 4 } = 1$
center: $( 8,0 )$; foci: $( 8 , \sqrt { 3 } ) , ( 8 , - \sqrt { 3 } )$; vertices: $( 8,2 ) , ( 8 , - 2 )$ 
C)  $\frac { x ^ { 2 } } { 64 } + ( y - 2 ) ^ { 2 } = 1$
center: $( 2,0 )$; foci: $( 2,3 \sqrt { 7 } ) , ( 2 , - 3 \sqrt { 7 } )$; vertices: $( 2,8 ) , ( 2 , - 8 )$ 
D)  $\frac { x ^ { 2 } } { 4 } + ( y - 8 ) ^ { 2 } = 1$
center: $( 8,0 )$; foci: $( 8 , \sqrt { 3 } ) , ( 8 , - 3 \sqrt { 7 } )$; vertices: $( 8,2 )$,
$( 8 , - 2 )$ A

Question 4

Find the vertex, focus, and directrix of the parabola with the given equation.
-$( x - 2 ) ^ { 2 } = - 20 ( y - 3 )$

Accepted Answer

A)  vertex: $ (2,3) $
focus: $ (2,-2) $
directrix: $ y=8 $ 
B)  vertex: $ (-2,-3) $
focus: $ (-2,-8) $
directrix: $ \mathrm{y}=2 $ 
C)  vertex: $ (2,3) $
focus: $ (2,8) $
directrix: $ x=-2 $ 
D)  vertex: $ (3,2) $
focus: $ (3,-3) $
directrix: $ y=7 $ 
A)  vertex: $ (2,3) $
focus: $ (2,-2) $
directrix: $ y=8 $ 
B)  vertex: $ (-2,-3) $
focus: $ (-2,-8) $
directrix: $ \mathrm{y}=2 $ 
C)  vertex: $ (2,3) $
focus: $ (2,8) $
directrix: $ x=-2 $ 
D)  vertex: $ (3,2) $
focus: $ (3,-3) $
directrix: $ y=7 $

Question 5

Identify the equation without applying a rotation of axes.
-$$4 x ^ { 2 } + 5 x y + 2 y ^ { 2 } + 2 x + 3 y - 5 = 0$$

Accepted Answer

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

Question 6

Find an equation of the parabola described.
-Directrix the line y = 3; vertex at (0, 0)

Accepted Answer

A)  $y = - \frac { 1 } { 12 } x ^ { 2 }$ 
B)  $y = - 12 x ^ { 2 }$ 
C)  $x = 3 y ^ { 2 }$ 
D)  $x = - \frac { 1 } { 12 } y ^ { 2 }$ 
A)  $y = - \frac { 1 } { 12 } x ^ { 2 }$ 
B)  $y = - 12 x ^ { 2 }$ 
C)  $x = 3 y ^ { 2 }$ 
D)  $x = - \frac { 1 } { 12 } y ^ { 2 }$

Question 7

Find an equation for the hyperbola described. Graph the equation.
-Center at $( 0,0 ) ;$ focus at $( \sqrt { 13 } , 0 )$;vertex at $( 2,0 )$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 25 } = 1$
  
B)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 25 } = 1$
  
C)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 4 } = 1$
  
D)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 4 } = 1$
  
A)  $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 25 } = 1$
  
B)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 25 } = 1$
  
C)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 4 } = 1$
  
D)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 4 } = 1$

Question 8

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

Accepted Answer

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

Question 9

Find the asymptotes of the hyperbola.
-$$\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$$

Accepted Answer

A)  $y = \frac { 4 } { 25 } x$ and $y = - \frac { 4 } { 25 } x$ 
B)  $y = \frac { 25 } { 4 } x$ and $y = - \frac { 25 } { 4 } x$ 
C)  $y = \frac { 2 } { 5 } x$ and $y = - \frac { 2 } { 5 } x$ 
D)  $y = \frac { 5 } { 2 } x$ and $y = - \frac { 5 } { 2 } x$ 
A)  $y = \frac { 4 } { 25 } x$ and $y = - \frac { 4 } { 25 } x$ 
B)  $y = \frac { 25 } { 4 } x$ and $y = - \frac { 25 } { 4 } x$ 
C)  $y = \frac { 2 } { 5 } x$ and $y = - \frac { 2 } { 5 } x$ 
D)  $y = \frac { 5 } { 2 } x$ and $y = - \frac { 5 } { 2 } x$

Question 10

Graph the hyperbola.
-$$\frac { ( y + 2 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 16 } = 1$$

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

Solve the problem.
-The orbit of a planet around a sun is an ellipse with the sun at one focus. The aphelion of a planet is its greatest distance from the sun, its perihelion is its shortest distance, and its mean distance is the length of the semimajor
Axis of the elliptical orbit. If a planet has a perihelion of 522.2 million miles and a mean distance of 525 million
Miles, write an equation for the orbit of the planet around the sun.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 519 ^ { 2 } } + \frac { y ^ { 2 } } { 516.9 ^ { 2 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 519 ^ { 2 } } + \frac { y ^ { 2 } } { 518.996 ^ { 2 } } = 1$ 
C)  $\frac { x ^ { 2 } } { 519.004 ^ { 2 } } + \frac { y ^ { 2 } } { 519 ^ { 2 } } = 1$ 
D)  $\frac { x ^ { 2 } } { 519 ^ { 2 } } + \frac { y ^ { 2 } } { 2.1 ^ { 2 } } = 1$ 
A)  $\frac { x ^ { 2 } } { 519 ^ { 2 } } + \frac { y ^ { 2 } } { 516.9 ^ { 2 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 519 ^ { 2 } } + \frac { y ^ { 2 } } { 518.996 ^ { 2 } } = 1$ 
C)  $\frac { x ^ { 2 } } { 519.004 ^ { 2 } } + \frac { y ^ { 2 } } { 519 ^ { 2 } } = 1$ 
D)  $\frac { x ^ { 2 } } { 519 ^ { 2 } } + \frac { y ^ { 2 } } { 2.1 ^ { 2 } } = 1$

Question 13

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

Accepted Answer

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

Question 14

Rotate the axes so that the new equation contains no xy-term. Graph the new equation.
-$x^{2}+x y+y^{2}-3 y-6=0$

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 15

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation.
-$17 x ^ { 2 } - 12 x y + 8 y ^ { 2 } - 68 x + 24 y - 12 = 0$

Accepted Answer

A)  $\theta = 26.6 ^ { \circ }$
$$\frac { x ^ { \prime 2 } } { 4 } + \frac { y ^ { \prime 2 } } { 16 } = 1$$
ellipse
center at $( 0,0 )$
major axis is $y ^ { \prime } -$ axis
vertices at $( 0 , \pm 4 )$ 
B)  $\theta = 63.4 ^ { \circ }$
$$\frac { \left( x ^ { \prime } - \frac { 2 \sqrt { 5 } } { 5 } \right) ^ { 2 } } { 16 } + \frac { \left( y ^ { \prime } + \frac { 4 \sqrt { 5 } } { 5 } \right) ^ { 2 } } { 4 } = 1$$
ellipse
center at $\left( \frac { 2 \sqrt { 5 } } { 5 } , - \frac { 4 \sqrt { 5 } } { 5 } \right)$
major axis is $x ^ { \prime }$-axis
vertices at $\left( 4 + \frac { 2 \sqrt { 5 } } { 5 } , - \frac { 4 \sqrt { 5 } } { 5 } \right)$ and $\left( - 4 + \frac { 2 \sqrt { 5 } } { 5 } , - \frac { 4 \sqrt { 5 } } { 5 } \right)$ 
C)  $\theta = 63.4 ^ { \circ }$
$x ^ { \prime 2 } = - 16 y ^ { \prime }$
parabola
vertex at $( 0,0 )$
focus at $( 0 , - 4 )$ 
D)  $\theta = 63.4 ^ { \circ }$
$$\frac { x ^ { \prime 2 } } { 16 } - \frac { y ^ { \prime 2 } } { 4 } = 1$$
hyperbola
center at $( 0,0 )$
transverse axis is the $x ^ { \prime }$-axis
vertices at $( \pm 4,0 )$ 
A)  $\theta = 26.6 ^ { \circ }$
$$\frac { x ^ { \prime 2 } } { 4 } + \frac { y ^ { \prime 2 } } { 16 } = 1$$
ellipse
center at $( 0,0 )$
major axis is $y ^ { \prime } -$ axis
vertices at $( 0 , \pm 4 )$ 
B)  $\theta = 63.4 ^ { \circ }$
$$\frac { \left( x ^ { \prime } - \frac { 2 \sqrt { 5 } } { 5 } \right) ^ { 2 } } { 16 } + \frac { \left( y ^ { \prime } + \frac { 4 \sqrt { 5 } } { 5 } \right) ^ { 2 } } { 4 } = 1$$
ellipse
center at $\left( \frac { 2 \sqrt { 5 } } { 5 } , - \frac { 4 \sqrt { 5 } } { 5 } \right)$
major axis is $x ^ { \prime }$-axis
vertices at $\left( 4 + \frac { 2 \sqrt { 5 } } { 5 } , - \frac { 4 \sqrt { 5 } } { 5 } \right)$ and $\left( - 4 + \frac { 2 \sqrt { 5 } } { 5 } , - \frac { 4 \sqrt { 5 } } { 5 } \right)$ 
C)  $\theta = 63.4 ^ { \circ }$
$x ^ { \prime 2 } = - 16 y ^ { \prime }$
parabola
vertex at $( 0,0 )$
focus at $( 0 , - 4 )$ 
D)  $\theta = 63.4 ^ { \circ }$
$$\frac { x ^ { \prime 2 } } { 16 } - \frac { y ^ { \prime 2 } } { 4 } = 1$$
hyperbola
center at $( 0,0 )$
transverse axis is the $x ^ { \prime }$-axis
vertices at $( \pm 4,0 )$

Question 16

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

Accepted Answer

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

Question 17

Find the asymptotes of the hyperbola.
-$$y ^ { 2 } - x ^ { 2 } = 9$$

Accepted Answer

A)  $y = \frac { 1 } { 9 } x$ and $y = - \frac { 1 } { 9 } x$ 
B)  $y = \frac { 1 } { 3 } x$ and $y = - \frac { 1 } { 3 } x$ 
C)  $y = x$ and $y = - x$ 
D)  $y = 3 x$ and $y = - 3 x$ 
A)  $y = \frac { 1 } { 9 } x$ and $y = - \frac { 1 } { 9 } x$ 
B)  $y = \frac { 1 } { 3 } x$ and $y = - \frac { 1 } { 3 } x$ 
C)  $y = x$ and $y = - x$ 
D)  $y = 3 x$ and $y = - 3 x$

Question 18

Graph the equation.
-$(y-1)^{2}=-7(x+2)$

Accepted Answer

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

Question 19

Find an equation of the parabola described and state the two points that define the latus rectum.
-Focus at $( 0,4 )$; directrix the line $y = - 4$

Accepted Answer

A)  $y ^ { 2 } = 4 x$; latus rectum: $( 9,2 )$ and $( - 9,2 )$ 
B)  $x ^ { 2 } = 4 y$; latus rectum: $( 2,4 )$ and $( - 2,4 )$ 
C)  $x ^ { 2 } = 16 y$; latus rectum: $( 8,4 )$ and $( - 8,4 )$ 
D)  $x ^ { 2 } = 16 y$; latus rectum: $( 4,8 )$ and $( - 4,8 )$ 
A)  $y ^ { 2 } = 4 x$; latus rectum: $( 9,2 )$ and $( - 9,2 )$ 
B)  $x ^ { 2 } = 4 y$; latus rectum: $( 2,4 )$ and $( - 2,4 )$ 
C)  $x ^ { 2 } = 16 y$; latus rectum: $( 8,4 )$ and $( - 8,4 )$ 
D)  $x ^ { 2 } = 16 y$; latus rectum: $( 4,8 )$ and $( - 4,8 )$

Question 20

Solve the problem.
-A comet follows the hyperbolic path described by $\frac { x ^ { 2 } } { 22 } - \frac { y ^ { 2 } } { 22 } = 1$, where $x$ and $y$ are in millions. If the sun is the fc of the path, how close to the sun is the vertex of the path?

Accepted Answer

A)  $2.1$ million 
B)  $5.3$ million 
C)  28 million 
D)  $3.2$ million 
A)  $2.1$ million 
B)  $5.3$ million 
C)  28 million 
D)  $3.2$ million

Find the center, foci, and vertices of the ellipse. - $2 x ^ { 2 } + 5 y ^ { 2 } - 12 x + 60 y + 188 = 0$

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

Find the center, foci, and vertices of the ellipse. - $16 x ^ { 2 } + y ^ { 2 } - 256 x + 1,008 = 0$

Find the vertex, focus, and directrix of the parabola with the given equation. - $( x - 2 ) ^ { 2 } = - 20 ( y - 3 )$

Identify the equation without applying a rotation of axes. - $4 x ^ { 2 } + 5 x y + 2 y ^ { 2 } + 2 x + 3 y - 5 = 0$

Find an equation of the parabola described. -Directrix the line y = 3; vertex at (0, 0)

Find an equation for the hyperbola described. Graph the equation. -Center at $( 0,0 ) ;$ focus at $( \sqrt { 13 } , 0 )$ ;vertex at $( 2,0 )$ $Find an equation for the hyperbola described. Graph the equation. -Center at ( 0,0 ) ; focus at ( \sqrt { 13 } , 0 ) ;vertex at ( 2,0 )$

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

Find the asymptotes of the hyperbola. - $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$

Graph the hyperbola. - $\frac { ( y + 2 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 16 } = 1$ $Graph the hyperbola. - \frac { ( y + 2 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 16 } = 1$

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

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

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - $x^{2}+x y+y^{2}-3 y-6=0$ $Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - x^{2}+x y+y^{2}-3 y-6=0$

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. - $17 x ^ { 2 } - 12 x y + 8 y ^ { 2 } - 68 x + 24 y - 12 = 0$

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

Find the asymptotes of the hyperbola. - $y ^ { 2 } - x ^ { 2 } = 9$

Graph the equation. - $(y-1)^{2}=-7(x+2)$ $Graph the equation. - (y-1)^{2}=-7(x+2)$

Find an equation of the parabola described and state the two points that define the latus rectum. -Focus at $( 0,4 )$ ; directrix the line $y = - 4$

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Exam 9: Analytic Geometry

Find the center, foci, and vertices of the ellipse. - 2x2+5y2−12x+60y+188=02 x ^ { 2 } + 5 y ^ { 2 } - 12 x + 60 y + 188 = 02x2+5y2−12x+60y+188=0

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 the center, foci, and vertices of the ellipse. - 16x2+y2−256x+1,008=016 x ^ { 2 } + y ^ { 2 } - 256 x + 1,008 = 016x2+y2−256x+1,008=0

Find the vertex, focus, and directrix of the parabola with the given equation. - (x−2)2=−20(y−3)( x - 2 ) ^ { 2 } = - 20 ( y - 3 )(x−2)2=−20(y−3)

Identify the equation without applying a rotation of axes. - 4x2+5xy+2y2+2x+3y−5=04 x ^ { 2 } + 5 x y + 2 y ^ { 2 } + 2 x + 3 y - 5 = 04x2+5xy+2y2+2x+3y−5=0

Find an equation of the parabola described. -Directrix the line y = 3; vertex at (0, 0)

Find an equation for the hyperbola described. Graph the equation. -Center at (0,0);( 0,0 ) ;(0,0); focus at (13,0)( \sqrt { 13 } , 0 )(13​,0) ;vertex at (2,0)( 2,0 )(2,0)

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

Find the asymptotes of the hyperbola. - x225−y29=1\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 125x2​−9y2​=1

Graph the hyperbola. - (y+2)29−(x−2)216=1\frac { ( y + 2 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 16 } = 19(y+2)2​−16(x−2)2​=1

Graph the hyperbola. - (x−2)24−(y−2)216=1\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y - 2 ) ^ { 2 } } { 16 } = 14(x−2)2​−16(y−2)2​=1

Graph the equation. - x2=12yx^{2}=12 yx2=12y

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - x2+xy+y2−3y−6=0x^{2}+x y+y^{2}-3 y-6=0x2+xy+y2−3y−6=0

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. - 17x2−12xy+8y2−68x+24y−12=017 x ^ { 2 } - 12 x y + 8 y ^ { 2 } - 68 x + 24 y - 12 = 017x2−12xy+8y2−68x+24y−12=0

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

Find the asymptotes of the hyperbola. - y2−x2=9y ^ { 2 } - x ^ { 2 } = 9y2−x2=9

Graph the equation. - (y−1)2=−7(x+2)(y-1)^{2}=-7(x+2)(y−1)2=−7(x+2)

Find an equation of the parabola described and state the two points that define the latus rectum. -Focus at (0,4)( 0,4 )(0,4) ; directrix the line y=−4y = - 4y=−4

Solve the problem. -A comet follows the hyperbolic path described by x222−y222=1\frac { x ^ { 2 } } { 22 } - \frac { y ^ { 2 } } { 22 } = 122x2​−22y2​=1 , where xxx and yyy are in millions. If the sun is the fc of the path, how close to the sun is the vertex of the path?

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

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Graphing Utilities

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Find the center, foci, and vertices of the ellipse. - $2 x ^ { 2 } + 5 y ^ { 2 } - 12 x + 60 y + 188 = 0$

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

Find the center, foci, and vertices of the ellipse. - $16 x ^ { 2 } + y ^ { 2 } - 256 x + 1,008 = 0$

Find the vertex, focus, and directrix of the parabola with the given equation. - $( x - 2 ) ^ { 2 } = - 20 ( y - 3 )$

Identify the equation without applying a rotation of axes. - $4 x ^ { 2 } + 5 x y + 2 y ^ { 2 } + 2 x + 3 y - 5 = 0$

Find an equation for the hyperbola described. Graph the equation. -Center at $( 0,0 ) ;$ focus at $( \sqrt { 13 } , 0 )$ ;vertex at $( 2,0 )$ $Find an equation for the hyperbola described. Graph the equation. -Center at ( 0,0 ) ; focus at ( \sqrt { 13 } , 0 ) ;vertex at ( 2,0 )$

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

Find the asymptotes of the hyperbola. - $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$

Graph the hyperbola. - $\frac { ( y + 2 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 16 } = 1$ $Graph the hyperbola. - \frac { ( y + 2 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 16 } = 1$

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

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

Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - $x^{2}+x y+y^{2}-3 y-6=0$ $Rotate the axes so that the new equation contains no xy-term. Graph the new equation. - x^{2}+x y+y^{2}-3 y-6=0$

Rotate the axes so that the new equation contains no xy-term. Discuss the new equation. - $17 x ^ { 2 } - 12 x y + 8 y ^ { 2 } - 68 x + 24 y - 12 = 0$

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

Find the asymptotes of the hyperbola. - $y ^ { 2 } - x ^ { 2 } = 9$

Graph the equation. - $(y-1)^{2}=-7(x+2)$ $Graph the equation. - (y-1)^{2}=-7(x+2)$

Find an equation of the parabola described and state the two points that define the latus rectum. -Focus at $( 0,4 )$ ; directrix the line $y = - 4$