Question 1

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

Accepted Answer

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

Question 2

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 3

Find an equation for the ellipse described. Graph the equation.
-Foci at (-1, 4) and (-5, 4); vertex at (-7, 4)

Accepted Answer

A)  $\frac { ( x + 4 ) ^ { 2 } } { 12 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$
  
B)  $\frac { ( x + 4 ) ^ { 2 } } { 16 } + \frac { ( y - 2 ) ^ { 2 } } { 12 } = 1$
  
C)  $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y + 4 ) ^ { 2 } } { 12 } = 1$
  
D)  $\frac { ( x - 2 ) ^ { 2 } } { 12 } + \frac { ( y + 4 ) ^ { 2 } } { 16 } = 1$
  
A)  $\frac { ( x + 4 ) ^ { 2 } } { 12 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$
  
B)  $\frac { ( x + 4 ) ^ { 2 } } { 16 } + \frac { ( y - 2 ) ^ { 2 } } { 12 } = 1$
  
C)  $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y + 4 ) ^ { 2 } } { 12 } = 1$
  
D)  $\frac { ( x - 2 ) ^ { 2 } } { 12 } + \frac { ( y + 4 ) ^ { 2 } } { 16 } = 1$

Question 4

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

Accepted Answer

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

Question 5

Rotate the axes so that the new equation contains no xy-term. Discuss the new equati
-$\mathrm { xy } + 16 = 0$

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 $y ^ { \prime }$-axis
vertices at $( 0 , \pm 4 \sqrt { 2 } )$ 
C)  $\theta = 45 ^ { \circ }$
$y ^ { \prime 2 } = - 32 x ^ { \prime }$
parabola
vertex at $( 0,0 )$
focus at $( - 8,0 )$ 
D)  $\theta = 36.9 ^ { \circ }$
$\frac { x ^ { \prime 2 } } { 4 } + \frac { y ^ { \prime 2 } } { 2 } = 1$
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 $y ^ { \prime }$-axis
vertices at $( 0 , \pm 4 \sqrt { 2 } )$ 
C)  $\theta = 45 ^ { \circ }$
$y ^ { \prime 2 } = - 32 x ^ { \prime }$
parabola
vertex at $( 0,0 )$
focus at $( - 8,0 )$ 
D)  $\theta = 36.9 ^ { \circ }$
$\frac { x ^ { \prime 2 } } { 4 } + \frac { y ^ { \prime 2 } } { 2 } = 1$
ellipse
center at $( 0,0 )$
major axis is the $x ^ { \prime }$-axis
vertices at $( \pm 2,0 )$

Question 6

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 7

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

Accepted Answer

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

Question 8

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 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)  $y ^ { 2 } - x ^ { 2 } = 49$; for $x$ in $- \infty < x < \infty$ 
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)  $y ^ { 2 } - x ^ { 2 } = 49$; for $x$ in $- \infty < x < \infty$

Question 10

Name the conic.
-

Accepted Answer

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

Question 11

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 12

Find an equation for the ellipse described.
-Center at $( 0,0 )$; focus at $( 5,0 )$; vertex at $( 7,0 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 24 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 24 } = 1$ 
C)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } = 1$ 
D)  $\frac { x ^ { 2 } } { 24 } + \frac { y ^ { 2 } } { 49 } = 1$ 
A)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 24 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 24 } = 1$ 
C)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } = 1$ 
D)  $\frac { x ^ { 2 } } { 24 } + \frac { y ^ { 2 } } { 49 } = 1$

Question 13

Find an equation for the ellipse described. Graph the equation.
-Foci at $( 3 , - 1 )$ and $( 3 , - 7 )$; length of major axis is 10

Accepted Answer

A) 
 
$\frac { ( y + 4 ) ^ { 2 } } { 25 } + \frac { ( x + 3 ) ^ { 2 } } { 16 } = 1$ 
B) 
 
$$\frac { ( x + 4 ) ^ { 2 } } { 16 } + \frac { ( y + 3 ) ^ { 2 } } { 25 } = 1$$ 
C) 
  
D) 
 
 (x + 4)2 + (y + 3)2 = 1 (y + 4)2 + (x - 3)2 = 1 25 16 25 16 
A) 
 
$\frac { ( y + 4 ) ^ { 2 } } { 25 } + \frac { ( x + 3 ) ^ { 2 } } { 16 } = 1$ 
B) 
 
$$\frac { ( x + 4 ) ^ { 2 } } { 16 } + \frac { ( y + 3 ) ^ { 2 } } { 25 } = 1$$ 
C) 
  
D) 
 
 (x + 4)2 + (y + 3)2 = 1 (y + 4)2 + (x - 3)2 = 1 25 16 25 16

Question 14

Find the vertex, focus, and directrix of the parabola. Graph the equation.
-$x^{2}-8 x=12 y-76$
 
 A)
vertex: $ (4,5) $
focus: $ (4,2) $
directrix: $ y=8 $

Accepted Answer

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 $
  
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 15

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

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 16

Match the equation to its graph.
-$$y ^ { 2 } = 13 x$$

Accepted Answer

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

Question 17

Find an equation of the parabola described.
-Vertex at (0, 0); axis of symmetry the x-axis; containing the point (9, 5) A) $y ^ { 2 } = \frac { 25 } { 36 } x$

Accepted Answer

B)  $y ^ { 2 } = \frac { 25 } { 9 } x$ 
C)  $x ^ { 2 } = \frac { 25 } { 36 } y$ 
D)  $x ^ { 2 } = \frac { 25 } { 9 } y$ 
B)  $y ^ { 2 } = \frac { 25 } { 9 } x$ 
C)  $x ^ { 2 } = \frac { 25 } { 36 } y$ 
D)  $x ^ { 2 } = \frac { 25 } { 9 } y$

Question 18

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

Accepted Answer

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

Question 19

Find an equation for the ellipse described. Graph the equation.
-Vertices at (5, -4) and (5, 8); length of minor axis is 6

Accepted Answer

A)

$\frac { ( x - 5 ) ^ { 2 } } { 36 } + \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$ 
B)

$\frac { ( x + 5 ) ^ { 2 } } { 9 } + \frac { ( y + 2 ) ^ { 2 } } { 36 } = 1$ 
C) 
 
$\frac { ( x + 5 ) ^ { 2 } } { 36 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$ 
D)

$$\frac { ( x - 5 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$$ 
A)

$\frac { ( x - 5 ) ^ { 2 } } { 36 } + \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$ 
B)

$\frac { ( x + 5 ) ^ { 2 } } { 9 } + \frac { ( y + 2 ) ^ { 2 } } { 36 } = 1$ 
C) 
 
$\frac { ( x + 5 ) ^ { 2 } } { 36 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$ 
D)

$$\frac { ( x - 5 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$$

Question 20

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

Accepted Answer

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

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 ellipse described. -Center at $( 0,0 )$ ; focus at $( - 3,0 )$ ; vertex at $( 4,0 )$

Find an equation for the ellipse described. Graph the equation. -Foci at (-1, 4) and (-5, 4); vertex at (-7, 4)

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 equati - $\mathrm { xy } + 16 = 0$

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

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

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

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

Name the conic. -

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

Find an equation for the ellipse described. -Center at $( 0,0 )$ ; focus at $( 5,0 )$ ; vertex at $( 7,0 )$

Find an equation for the ellipse described. Graph the equation. -Foci at $( 3 , - 1 )$ and $( 3 , - 7 )$ ; length of major axis is 10

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

Match the equation to its graph. - $y ^ { 2 } = 13 x$

Find an equation of the parabola described. -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) $x ^ { 2 } = \frac { 25 } { 9 } y$

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

Find an equation for the ellipse described. Graph the equation. -Vertices at (5, -4) and (5, 8); length of minor axis is 6

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

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

Review

Filters

Exam 9: Analytic Geometry

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

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)

Find an equation for the ellipse described. Graph the equation. -Foci at (-1, 4) and (-5, 4); vertex at (-7, 4)

Graph the hyperbola. - y24−x216=1\frac{y^{2}}{4}-\frac{x^{2}}{16}=14y2​−16x2​=1

Rotate the axes so that the new equation contains no xy-term. Discuss the new equati - xy+16=0\mathrm { xy } + 16 = 0xy+16=0

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

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

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

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

Name the conic. -

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

Find an equation for the ellipse described. -Center at (0,0)( 0,0 )(0,0) ; focus at (5,0)( 5,0 )(5,0) ; vertex at (7,0)( 7,0 )(7,0)

Find an equation for the ellipse described. Graph the equation. -Foci at (3,−1)( 3 , - 1 )(3,−1) and (3,−7)( 3 , - 7 )(3,−7) ; length of major axis is 10

Find the center, foci, and vertices of the ellipse. - 16(x+2)2+9(y−1)2=14416 ( \mathrm { x } + 2 ) ^ { 2 } + 9 ( \mathrm { y } - 1 ) ^ { 2 } = 14416(x+2)2+9(y−1)2=144

Match the equation to its graph. - y2=13xy ^ { 2 } = 13 xy2=13x

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

Find an equation for the ellipse described. Graph the equation. -Vertices at (5, -4) and (5, 8); length of minor axis is 6

Graph the curve whose parametric equations are given. - x=2sin⁡t,y=2cos⁡t;0≤t≤2πx=2 \sin t, y=2 \cos t ; 0 \leq t \leq 2 \pix=2sint,y=2cost;0≤t≤2π

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

Review

Filters

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 ellipse described. -Center at $( 0,0 )$ ; focus at $( - 3,0 )$ ; vertex at $( 4,0 )$

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 equati - $\mathrm { xy } + 16 = 0$

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

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

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

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

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

Find an equation for the ellipse described. -Center at $( 0,0 )$ ; focus at $( 5,0 )$ ; vertex at $( 7,0 )$

Find an equation for the ellipse described. Graph the equation. -Foci at $( 3 , - 1 )$ and $( 3 , - 7 )$ ; length of major axis is 10

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

Match the equation to its graph. - $y ^ { 2 } = 13 x$

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

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