Question 1

Graph the curve whose parametric equations are given.
-$x=2 t, y=t+5 ;-2 \leq t \leq 3$

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Find the vertex, focus, and directrix of the parabola with the given equation.
-$$( y - 4 ) ^ { 2 } = - 8 ( x + 2 )$$

Accepted Answer

A)  vertex: $( - 2,4 )$
focus: $( 0,4 )$
directrix: $x = - 4$ 
B)  vertex: $( 4 , - 2 )$
focus: $( 2,-2 )$
directrix: $x = 6$ 
C)  vertex: $( 2 , - 4 )$
focus: $( 0,-4 )$
directrix: $x = 4$ 
D)  vertex: $( - 2,4 )$
focus: $( - 4,4 )$
directrix: $x = 0$ 
A)  vertex: $( - 2,4 )$
focus: $( 0,4 )$
directrix: $x = - 4$ 
B)  vertex: $( 4 , - 2 )$
focus: $( 2,-2 )$
directrix: $x = 6$ 
C)  vertex: $( 2 , - 4 )$
focus: $( 0,-4 )$
directrix: $x = 4$ 
D)  vertex: $( - 2,4 )$
focus: $( - 4,4 )$
directrix: $x = 0$

Question 4

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 5

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
-$25 y ^ { 2 } - 16 x ^ { 2 } = 400$

Accepted Answer

A)  center at $ (0,0) $
transverse axis is $ x $-axis
vertices: $ (-5,0),(5,0) $
foci: $ (-\sqrt{41}, 0),(\sqrt{41}, 0) $
asymptotes of $ y=-\frac{4}{5} $ and $ y=\frac{4}{5} $ 
B)  center at $ (0,0) $
transverse axis is $ x $-axis
vertices: $ (-4,0),(4,0) $
foci: $ (-5,0),(5,0) $
asymptotes of $ y=-\frac{4}{5} $ and $ y=\frac{4}{5} $ 
C) center at $ (0,0) $
transverse axis is $ \mathrm{y} $-axis
vertices: $ (0,-4),(0,4) $
foci: $ (-\sqrt{41}, 0),(\sqrt{41}, 0) $
asymptotes of $ y=-\frac{4}{5} $ and $ y=\frac{4}{5} $ 
D) center at $ (0,0) $
transverse axis is $ y $-axis
vertices at $ (0,-4) $ and $ (0,4) $
foci at $ (0,-\sqrt{41}) $ and $ (0, \sqrt{41}) $
asymptotes of $ y=-\frac{4}{5} $ and $ y=\frac{4}{5} $ 
A)  center at $ (0,0) $
transverse axis is $ x $-axis
vertices: $ (-5,0),(5,0) $
foci: $ (-\sqrt{41}, 0),(\sqrt{41}, 0) $
asymptotes of $ y=-\frac{4}{5} $ and $ y=\frac{4}{5} $ 
B)  center at $ (0,0) $
transverse axis is $ x $-axis
vertices: $ (-4,0),(4,0) $
foci: $ (-5,0),(5,0) $
asymptotes of $ y=-\frac{4}{5} $ and $ y=\frac{4}{5} $ 
C) center at $ (0,0) $
transverse axis is $ \mathrm{y} $-axis
vertices: $ (0,-4),(0,4) $
foci: $ (-\sqrt{41}, 0),(\sqrt{41}, 0) $
asymptotes of $ y=-\frac{4}{5} $ and $ y=\frac{4}{5} $ 
D) center at $ (0,0) $
transverse axis is $ y $-axis
vertices at $ (0,-4) $ and $ (0,4) $
foci at $ (0,-\sqrt{41}) $ and $ (0, \sqrt{41}) $
asymptotes of $ y=-\frac{4}{5} $ and $ y=\frac{4}{5} $

Question 6

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

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 7

Solve the problem.
-A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 174 feet and a maximum height of 30 feet. Find the height of the arch at 15 feet from its center.

Accepted Answer

A)  3.6 ft 
B)  21.8 ft 
C)  0.2 ft 
D)  29.1 ft 
A)  3.6 ft 
B)  21.8 ft 
C)  0.2 ft 
D)  29.1 ft

Question 8

Write an equation for the hyperbola.
-

Accepted Answer

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

Question 9

Graph the equation.
-$x^{2}=-18 y$

Accepted Answer

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

Question 10

Find an equation for the ellipse described.
-Vertices at $( - 4,5 )$ and $( 16,5 ) ;$ focus at $( 14,5 )$

Accepted Answer

A)  $\frac { ( x + 6 ) ^ { 2 } } { 9 } + \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x - 6 ) ^ { 2 } } { 49 } - \frac { ( y + 2 ) ^ { 2 } } { 19 } = 1$ 
C)  $\frac { ( x - 6 ) ^ { 2 } } { 100 } + \frac { ( y - 5 ) ^ { 2 } } { 36 } = 1$ 
D)  $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 6 ) ^ { 2 } } { 15 } = 1$ 
A)  $\frac { ( x + 6 ) ^ { 2 } } { 9 } + \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x - 6 ) ^ { 2 } } { 49 } - \frac { ( y + 2 ) ^ { 2 } } { 19 } = 1$ 
C)  $\frac { ( x - 6 ) ^ { 2 } } { 100 } + \frac { ( y - 5 ) ^ { 2 } } { 36 } = 1$ 
D)  $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 6 ) ^ { 2 } } { 15 } = 1$

Question 11

Find an equation for the hyperbola described.
-Vertices at $( 0 , \pm 10 )$; asymptotes at $y = \pm \frac { 5 } { 3 } x$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 36 } = 1$ 
B)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$ 
C)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 100 } = 1$ 
D)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 9 } = 1$ 
A)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 36 } = 1$ 
B)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$ 
C)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 100 } = 1$ 
D)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 9 } = 1$

Question 12

Graph the ellipse and locate the foci.
-$16 x^{2}+9 y^{2}=144$

Accepted Answer

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

Question 13

Identify the equation without applying a rotation of axes.
-$$10 x ^ { 2 } + 9 x y + 4 y ^ { 2 } + 2 x - 3 y + 5 = 0$$

Accepted Answer

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

Question 14

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
-$$\frac { ( x - 4 ) ^ { 2 } } { 25 } - \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1$$

Accepted Answer

A)  center at $( 4 , - 1 )$
transverse axis is parallel to $x$-axis
vertices at $( 0 , - 1 )$ and $( 8 , - 1 )$
foci at $( 4 - \sqrt { 41 } , - 1 )$ and $( 4 + \sqrt { 41 } , - 1 )$
asymptotes of $y + 1 = - \frac { 5 } { 4 } ( x - 4 )$ and $y + 1 = \frac { 5 } { 4 } ( x - 4 )$ 
B)  center at $( - 1,4 )$
transverse axis is parallel to $x$-axis
vertices at $( - 6,4 )$ and $( 4,4 )$
foci at $( - 1 - \sqrt { 41 } , 4 )$ and $( - 1 + \sqrt { 41 } , 4 )$
asymptotes of $y - 4 = - \frac { 4 } { 5 } ( x + 1 )$ and $y - 4 = \frac { 4 } { 5 } ( x + 1 )$ 
C)  center at $( 4 , - 1 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices at $( 4 , - 6 )$ and $( 4,4 )$
foci at $( 4 , - 1 - \sqrt { 41 } )$ and $( 4 , - 1 + \sqrt { 41 } )$
asymptotes of $y - 1 = - \frac { 5 } { 4 } ( x + 4 )$ and $y - 1 = \frac { 5 } { 4 } ( x + 4 )$ 
D)  center at $( 4 , - 1 )$
transverse axis is parallel to $x$-axis
vertices at $( - 1 , - 1 )$ and $( 9 , - 1 )$
foci at $( 4 - \sqrt { 41 } , - 1 )$ and $( 4 + \sqrt { 41 } , - 1 )$
asymptotes of $y + 1 = - \frac { 4 } { 5 } ( x - 4 )$ and $y + 1 = \frac { 4 } { 5 } ( x - 4 )$ 
A)  center at $( 4 , - 1 )$
transverse axis is parallel to $x$-axis
vertices at $( 0 , - 1 )$ and $( 8 , - 1 )$
foci at $( 4 - \sqrt { 41 } , - 1 )$ and $( 4 + \sqrt { 41 } , - 1 )$
asymptotes of $y + 1 = - \frac { 5 } { 4 } ( x - 4 )$ and $y + 1 = \frac { 5 } { 4 } ( x - 4 )$ 
B)  center at $( - 1,4 )$
transverse axis is parallel to $x$-axis
vertices at $( - 6,4 )$ and $( 4,4 )$
foci at $( - 1 - \sqrt { 41 } , 4 )$ and $( - 1 + \sqrt { 41 } , 4 )$
asymptotes of $y - 4 = - \frac { 4 } { 5 } ( x + 1 )$ and $y - 4 = \frac { 4 } { 5 } ( x + 1 )$ 
C)  center at $( 4 , - 1 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices at $( 4 , - 6 )$ and $( 4,4 )$
foci at $( 4 , - 1 - \sqrt { 41 } )$ and $( 4 , - 1 + \sqrt { 41 } )$
asymptotes of $y - 1 = - \frac { 5 } { 4 } ( x + 4 )$ and $y - 1 = \frac { 5 } { 4 } ( x + 4 )$ 
D)  center at $( 4 , - 1 )$
transverse axis is parallel to $x$-axis
vertices at $( - 1 , - 1 )$ and $( 9 , - 1 )$
foci at $( 4 - \sqrt { 41 } , - 1 )$ and $( 4 + \sqrt { 41 } , - 1 )$
asymptotes of $y + 1 = - \frac { 4 } { 5 } ( x - 4 )$ and $y + 1 = \frac { 4 } { 5 } ( x - 4 )$

Question 15

Find an equation for the ellipse described.
-Center at $( 0,0 ) ;$ focus at $( 0 , - 2 ) ;$ vertex at $( 0,6 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 32 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 36 } = 1$ 
C)  $\frac { x ^ { 2 } } { 32 } + \frac { y ^ { 2 } } { 36 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 32 } = 1$ 
A)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 32 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 36 } = 1$ 
C)  $\frac { x ^ { 2 } } { 32 } + \frac { y ^ { 2 } } { 36 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 32 } = 1$

Question 16

Name the conic.
-

Accepted Answer

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

Question 17

Identify the conic that the polar equation represents. Also, give the position of the directrix.
-$$r = \frac { 6 } { 3 - 4 \cos \theta }$$

Accepted Answer

A)  ellipse, directrix is perpendicular to the polar axis at a distance $\frac { 3 } { 2 }$ units to the right of the pole 
B)  hyperbola, directrix is perpendicular to the polar axis at a distance 3 units to the right of the pole 
C)  hyperbola, directrix is perpendicular to the polar axis at a distance $\frac { 3 } { 2 }$ units to the left of the pole 
D)  ellipse, directrix is perpendicular to the polar axis at a distance 3 units to the left of the pole 
A)  ellipse, directrix is perpendicular to the polar axis at a distance $\frac { 3 } { 2 }$ units to the right of the pole 
B)  hyperbola, directrix is perpendicular to the polar axis at a distance 3 units to the right of the pole 
C)  hyperbola, directrix is perpendicular to the polar axis at a distance $\frac { 3 } { 2 }$ units to the left of the pole 
D)  ellipse, directrix is perpendicular to the polar axis at a distance 3 units to the left of the pole

Question 18

Convert the polar equation to a rectangular equation.
-$$r = \frac { 4 \sec \theta } { \sec \theta + 2 }$$

Accepted Answer

A)  $3 x ^ { 2 } - y ^ { 2 } - 16 x + 16 = 0$ 
B)  $3 y ^ { 2 } - x ^ { 2 } + 16 = 0$ 
C)  $3 x ^ { 2 } - y ^ { 2 } + 16 = 0$ 
D)  $3 y ^ { 2 } - x ^ { 2 } - 16 y + 16 = 0$ 
A)  $3 x ^ { 2 } - y ^ { 2 } - 16 x + 16 = 0$ 
B)  $3 y ^ { 2 } - x ^ { 2 } + 16 = 0$ 
C)  $3 x ^ { 2 } - y ^ { 2 } + 16 = 0$ 
D)  $3 y ^ { 2 } - x ^ { 2 } - 16 y + 16 = 0$

Question 19

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

Accepted Answer

A) vertex: $ (0,0) $
focus: $ (-3,0) $
directrix: $ x=3 $ 
   
B)   vertex: $ (0,0) $
focus: $ (3,0) $
directrix: $ x=-3 $

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

C)  vertex: $ (0,0) $
focus: $ (0,-3) $
directrix: $ y=3 $
  
D)  vertex: $ (0,0) $
focus: $ (0,-3) $
directrix: $ y=3 $

Question 20

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.
-$x=3 \cos t, y=2 \sin t ; 0 \leq t \leq 2 \pi$

Accepted Answer

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

Graph the curve whose parametric equations are given. - $x=2 t, y=t+5 ;-2 \leq t \leq 3$ $Graph the curve whose parametric equations are given. - x=2 t, y=t+5 ;-2 \leq t \leq 3$

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

Find the vertex, focus, and directrix of the parabola with the given equation. - $( y - 4 ) ^ { 2 } = - 8 ( x + 2 )$

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

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $25 y ^ { 2 } - 16 x ^ { 2 } = 400$

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

Solve the problem. -A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 174 feet and a maximum height of 30 feet. Find the height of the arch at 15 feet from its center.

Write an equation for the hyperbola. -

Graph the equation. - $x^{2}=-18 y$ $Graph the equation. - x^{2}=-18 y$

Find an equation for the ellipse described. -Vertices at $( - 4,5 )$ and $( 16,5 ) ;$ focus at $( 14,5 )$

Find an equation for the hyperbola described. -Vertices at $( 0 , \pm 10 )$ ; asymptotes at $y = \pm \frac { 5 } { 3 } x$

Graph the ellipse and locate the foci. - $16 x^{2}+9 y^{2}=144$ $Graph the ellipse and locate the foci. - 16 x^{2}+9 y^{2}=144$

Identify the equation without applying a rotation of axes. - $10 x ^ { 2 } + 9 x y + 4 y ^ { 2 } + 2 x - 3 y + 5 = 0$

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $\frac { ( x - 4 ) ^ { 2 } } { 25 } - \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1$

Find an equation for the ellipse described. -Center at $( 0,0 ) ;$ focus at $( 0 , - 2 ) ;$ vertex at $( 0,6 )$

Name the conic. -

Identify the conic that the polar equation represents. Also, give the position of the directrix. - $r = \frac { 6 } { 3 - 4 \cos \theta }$

Convert the polar equation to a rectangular equation. - $r = \frac { 4 \sec \theta } { \sec \theta + 2 }$

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

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

Graph the curve whose parametric equations are given. - x=2t,y=t+5;−2≤t≤3x=2 t, y=t+5 ;-2 \leq t \leq 3x=2t,y=t+5;−2≤t≤3

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

Find the vertex, focus, and directrix of the parabola with the given equation. - (y−4)2=−8(x+2)( y - 4 ) ^ { 2 } = - 8 ( x + 2 )(y−4)2=−8(x+2)

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 the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - 25y2−16x2=40025 y ^ { 2 } - 16 x ^ { 2 } = 40025y2−16x2=400

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

Solve the problem. -A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 174 feet and a maximum height of 30 feet. Find the height of the arch at 15 feet from its center.

Write an equation for the hyperbola. -

Graph the equation. - x2=−18yx^{2}=-18 yx2=−18y

Find an equation for the ellipse described. -Vertices at (−4,5)( - 4,5 )(−4,5) and (16,5);( 16,5 ) ;(16,5); focus at (14,5)( 14,5 )(14,5)

Find an equation for the hyperbola described. -Vertices at (0,±10)( 0 , \pm 10 )(0,±10) ; asymptotes at y=±53xy = \pm \frac { 5 } { 3 } xy=±35​x

Graph the ellipse and locate the foci. - 16x2+9y2=14416 x^{2}+9 y^{2}=14416x2+9y2=144

Identify the equation without applying a rotation of axes. - 10x2+9xy+4y2+2x−3y+5=010 x ^ { 2 } + 9 x y + 4 y ^ { 2 } + 2 x - 3 y + 5 = 010x2+9xy+4y2+2x−3y+5=0

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - (x−4)225−(y+1)216=1\frac { ( x - 4 ) ^ { 2 } } { 25 } - \frac { ( y + 1 ) ^ { 2 } } { 16 } = 125(x−4)2​−16(y+1)2​=1

Find an equation for the ellipse described. -Center at (0,0);( 0,0 ) ;(0,0); focus at (0,−2);( 0 , - 2 ) ;(0,−2); vertex at (0,6)( 0,6 )(0,6)

Name the conic. -

Identify the conic that the polar equation represents. Also, give the position of the directrix. - r=63−4cos⁡θr = \frac { 6 } { 3 - 4 \cos \theta }r=3−4cosθ6​

Convert the polar equation to a rectangular equation. - r=4sec⁡θsec⁡θ+2r = \frac { 4 \sec \theta } { \sec \theta + 2 }r=secθ+24secθ​

Find the vertex, focus, and directrix of the parabola. - y2=−12xy^{2}=-12 xy2=−12x

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=3cos⁡t,y=2sin⁡t;0≤t≤2πx=3 \cos t, y=2 \sin t ; 0 \leq t \leq 2 \pix=3cost,y=2sint;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

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Graph the curve whose parametric equations are given. - $x=2 t, y=t+5 ;-2 \leq t \leq 3$ $Graph the curve whose parametric equations are given. - x=2 t, y=t+5 ;-2 \leq t \leq 3$

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

Find the vertex, focus, and directrix of the parabola with the given equation. - $( y - 4 ) ^ { 2 } = - 8 ( x + 2 )$

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

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $25 y ^ { 2 } - 16 x ^ { 2 } = 400$

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

Graph the equation. - $x^{2}=-18 y$ $Graph the equation. - x^{2}=-18 y$

Find an equation for the ellipse described. -Vertices at $( - 4,5 )$ and $( 16,5 ) ;$ focus at $( 14,5 )$

Find an equation for the hyperbola described. -Vertices at $( 0 , \pm 10 )$ ; asymptotes at $y = \pm \frac { 5 } { 3 } x$

Graph the ellipse and locate the foci. - $16 x^{2}+9 y^{2}=144$ $Graph the ellipse and locate the foci. - 16 x^{2}+9 y^{2}=144$

Identify the equation without applying a rotation of axes. - $10 x ^ { 2 } + 9 x y + 4 y ^ { 2 } + 2 x - 3 y + 5 = 0$

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $\frac { ( x - 4 ) ^ { 2 } } { 25 } - \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1$

Find an equation for the ellipse described. -Center at $( 0,0 ) ;$ focus at $( 0 , - 2 ) ;$ vertex at $( 0,6 )$

Identify the conic that the polar equation represents. Also, give the position of the directrix. - $r = \frac { 6 } { 3 - 4 \cos \theta }$

Convert the polar equation to a rectangular equation. - $r = \frac { 4 \sec \theta } { \sec \theta + 2 }$

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