Question 1

Write the word or phrase that best completes each statement or answers the question.
-$$9 x ^ { 2 } + 49 y ^ { 2 } = 11,025$$

Accepted Answer

A)  $x$-intercepts $\pm 1225$; y-intercepts $\pm 225$ 
B)  $x$-intercepts $\pm 15 ; y$-intercepts $\pm 35$ 
C)  $x$-intercepts $\pm 35$; $y$-intercepts $\pm 15$ 
D)  $x$-intercepts $\pm 225$; $y$-intercepts $\pm 1225$ 
A)  $x$-intercepts $\pm 1225$; y-intercepts $\pm 225$ 
B)  $x$-intercepts $\pm 15 ; y$-intercepts $\pm 35$ 
C)  $x$-intercepts $\pm 35$; $y$-intercepts $\pm 15$ 
D)  $x$-intercepts $\pm 225$; $y$-intercepts $\pm 1225$

Question 2

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.
-$x - 2 = ( y - 8 ) ^ { 2 }$

Accepted Answer

A)  $y = \sqrt { x - 2 } + 8$ and $y = 8 - \sqrt { x - 2 }$ 
B)  $y = \sqrt { x - 2 } + 8$ and $y = - \sqrt { x + 2 } - 8$ 
C)  $y = \sqrt { x - 2 } + 8$ and $y = 8 - \sqrt { x + 2 }$ 
D)  $y = \sqrt { x + 62 }$ and $y = - \sqrt { x - 66 }$ 
A)  $y = \sqrt { x - 2 } + 8$ and $y = 8 - \sqrt { x - 2 }$ 
B)  $y = \sqrt { x - 2 } + 8$ and $y = - \sqrt { x + 2 } - 8$ 
C)  $y = \sqrt { x - 2 } + 8$ and $y = 8 - \sqrt { x + 2 }$ 
D)  $y = \sqrt { x + 62 }$ and $y = - \sqrt { x - 66 }$

Question 3

Identify the type of graph.
-$$- x ^ { 2 } - 2 x + 4 y ^ { 2 } + 8 y = 20$$

Accepted Answer

A)  The equation has no graph. 
B)  The graph is an ellipse with center $\left( - \frac { 4 } { 5 } , \frac { 2 } { 5 } \right)$. 
C)  The graph is a circle with center $\left( \frac { 4 } { 5 } , - \frac { 2 } { 5 } \right)$. 
D)  The graph is a hyperbola opening to the right and left. 
A)  The equation has no graph. 
B)  The graph is an ellipse with center $\left( - \frac { 4 } { 5 } , \frac { 2 } { 5 } \right)$. 
C)  The graph is a circle with center $\left( \frac { 4 } { 5 } , - \frac { 2 } { 5 } \right)$. 
D)  The graph is a hyperbola opening to the right and left.

Question 4

Give the focus, directrix, and axis for the parabola.
-$$x = 9 y ^ { 2 }$$

Accepted Answer

A)  $\left( \frac { 1 } { 36 } , 0 \right) , x = \frac { 1 } { 36 } , x$-axis 
B)  $\left( \frac { 1 } { 36 } , 0 \right) , x = - \frac { 1 } { 36 } , x$-axis 
C)  $\left( 0 , \frac { 1 } { 36 } \right) , y = - \frac { 1 } { 36 } , y$-axis 
D)  $\left( \frac { 1 } { 9 } , 0 \right) , x = - \frac { 1 } { 9 } , x - a x i s$ 
A)  $\left( \frac { 1 } { 36 } , 0 \right) , x = \frac { 1 } { 36 } , x$-axis 
B)  $\left( \frac { 1 } { 36 } , 0 \right) , x = - \frac { 1 } { 36 } , x$-axis 
C)  $\left( 0 , \frac { 1 } { 36 } \right) , y = - \frac { 1 } { 36 } , y$-axis 
D)  $\left( \frac { 1 } { 9 } , 0 \right) , x = - \frac { 1 } { 9 } , x - a x i s$

Question 5

Give the focus, directrix, and axis for the parabola.
-$$( y + 3 ) ^ { 2 } = 4 ( x + 2 )$$

Accepted Answer

A)  $( - 2 , - 2 ) , x = - 4 , y = - 2$ 
B)  $( - 1 , - 3 ) , x = - 3 , y = - 3$ 
C)  $( 3,3 ) , x = 1 , y = 3$ 
D)  $( - 3 , - 3 ) , x = - 1 , y = - 3$ 
A)  $( - 2 , - 2 ) , x = - 4 , y = - 2$ 
B)  $( - 1 , - 3 ) , x = - 3 , y = - 3$ 
C)  $( 3,3 ) , x = 1 , y = 3$ 
D)  $( - 3 , - 3 ) , x = - 1 , y = - 3$

Question 6

Find the eccentricity of the hyperbola.
-$$x ^ { 2 } - 25 y ^ { 2 } = 25$$

Accepted Answer

A)  $\sqrt { 26 }$ 
B)  $\frac { 2 \sqrt { 6 } } { 5 }$ 
C)  $2 \sqrt { 6 }$ 
D)  $\frac { \sqrt { 26 } } { 5 }$ 
A)  $\sqrt { 26 }$ 
B)  $\frac { 2 \sqrt { 6 } } { 5 }$ 
C)  $2 \sqrt { 6 }$ 
D)  $\frac { \sqrt { 26 } } { 5 }$

Question 7

Give the focus, directrix, and axis for the parabola.
-$$( y - 5 ) ^ { 2 } = - 12 ( x + 2 )$$

Accepted Answer

A)  $( - 5,2 ) , x = 1 , y = 5$ 
B)  $( - 5,5 ) , x = - 2 , y = 5$ 
C)  $( - 5,5 ) , x = 1 , y = 5$ 
D)  $( - 5,5 ) , x = 1 , y = - 2$ 
A)  $( - 5,2 ) , x = 1 , y = 5$ 
B)  $( - 5,5 ) , x = - 2 , y = 5$ 
C)  $( - 5,5 ) , x = 1 , y = 5$ 
D)  $( - 5,5 ) , x = 1 , y = - 2$

Question 8

Solve the problem.
-An elliptical riding path is to be built on a rectangular piece of property that measures 10 mi by 4 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4
Sides

Accepted Answer

A)  $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 100 } = 1$ 
A)  $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 100 } = 1$

Question 9

Write the word or phrase that best completes each statement or answers the question.
-$$\frac { x ^ { 2 } } { 16 } = 1 - \frac { y ^ { 2 } } { 36 }$$

Accepted Answer

A)  $x$-intercepts $\pm 36 ; y$-intercepts $\pm 16$ 
B)  $x$-intercepts $\pm 6$; $y$-intercepts $\pm 4$ 
C)  $x$-intercepts $\pm 4 ; y$-intercepts $\pm 6$ 
D)  $x$-intercepts $\pm 16$; $y$-intercepts $\pm 36$ 
A)  $x$-intercepts $\pm 36 ; y$-intercepts $\pm 16$ 
B)  $x$-intercepts $\pm 6$; $y$-intercepts $\pm 4$ 
C)  $x$-intercepts $\pm 4 ; y$-intercepts $\pm 6$ 
D)  $x$-intercepts $\pm 16$; $y$-intercepts $\pm 36$

Question 10

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

Accepted Answer

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

Question 11

Graph the ellipse.
-$$\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 49 } = 1$$

Accepted Answer

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

Question 12

Identify the type of graph.
-$$\frac { ( x - 7 ) ^ { 2 } } { 4 } + \frac { ( y - 6 ) ^ { 2 } } { 9 } = 0$$

Accepted Answer

A)  The graph is an ellipse with center at $( - 7 , - 6 )$. 
B)  The graph is the point $( 7,6 )$. 
C)  The graph is an ellipse with center at $( 7,6 )$. 
D)  The graph is a hyperbola opening right and left. 
A)  The graph is an ellipse with center at $( - 7 , - 6 )$. 
B)  The graph is the point $( 7,6 )$. 
C)  The graph is an ellipse with center at $( 7,6 )$. 
D)  The graph is a hyperbola opening right and left.

Question 13

Identify the equation as a parabola, circle, ellipse, or hyperbola.
-$$y ^ { 2 } = 144 - x ^ { 2 }$$

Accepted Answer

A)  Circle 
B)  Ellipse 
C)  Hyperbola 
D)  Parabola 
A)  Circle 
B)  Ellipse 
C)  Hyperbola 
D)  Parabola

Question 14

Write the word or phrase that best completes each statement or answers the question.
-To graph $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 36 } = 1$ on a graphics calculator, we must consider the union of the graphs of the two functions, $y _ { 1 } = 6 \sqrt { \frac { x ^ { 2 } } { 16 } - 1 }$ and $y _ { 2 } = - 6 \sqrt { \frac { x ^ { 2 } } { 16 } - 1 }$. Using the graph of $y = \frac { x ^ { 2 } } { 16 } - 1$, explain (a) how the solution set of $\frac { x ^ { 2 } } { 16 } - 1 \geq 0$ can be determined graphically and (b) how it relates to the domain of the hyperbola.

Accepted Answer

The graph of @#LAT-DLM& lies above or on

Question 15

Graph the parabola.
-

Accepted Answer

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

Question 16

Identify the equation as a parabola, circle, ellipse, or hyperbola.
-$$4 x = 3 y ^ { 2 } - 31$$

Accepted Answer

A)  Circle 
B)  Hyperbola 
C)  Parabola 
D)  Ellipse 
A)  Circle 
B)  Hyperbola 
C)  Parabola 
D)  Ellipse

Question 17

Match the equation of the parabola with the appropriate description.
-$$x = 2 y ^ { 2 } - 6 y + 2$$

Accepted Answer

A)  Opens down 
B)  Opens left 
C)  Opens up 
D)  Opens right 
A)  Opens down 
B)  Opens left 
C)  Opens up 
D)  Opens right

Question 18

Solve the problem.
-A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is 18 ft and the vertical clearance must be 12 ft at a point 5 ft from the center. Find an equation for the ellipse.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 324 } = 1$ 
B)  $\frac { x ^ { 2 } } { 45 } + \frac { y ^ { 2 } } { 324 } = 1$ 
C)  $\frac { x ^ { 2 } } { 45 } + \frac { y ^ { 2 } } { 144 } = 1$ 
D)  $\frac { x ^ { 2 } } { 324 } + \frac { y ^ { 2 } } { 45 } = 1$ 
A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 324 } = 1$ 
B)  $\frac { x ^ { 2 } } { 45 } + \frac { y ^ { 2 } } { 324 } = 1$ 
C)  $\frac { x ^ { 2 } } { 45 } + \frac { y ^ { 2 } } { 144 } = 1$ 
D)  $\frac { x ^ { 2 } } { 324 } + \frac { y ^ { 2 } } { 45 } = 1$

Question 19

Identify the equation as a parabola, circle, ellipse, or hyperbola.
-$$16 x ^ { 2 } + 9 y ^ { 2 } = 144$$

Accepted Answer

A)  Hyperbola 
B)  Circle 
C)  Ellipse 
D)  Parabola 
A)  Hyperbola 
B)  Circle 
C)  Ellipse 
D)  Parabola

Question 20

Determine the two equations necessary to graph the ellipse with a graphing calculator.
-$$\frac { ( x - 3 ) ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 64 } = 1$$

Accepted Answer

A)  $y = \frac { 8 \sqrt { 9 - x ^ { 2 } } } { 9 }$ and $y = - \frac { 8 \sqrt { 9 - x ^ { 2 } } } { 9 }$ 
B)  $y = \frac { 8 \sqrt { - x ^ { 2 } + 6 x + 72 } } { 9 }$ and $y = - \frac { 8 \sqrt { - x ^ { 2 } + 6 x + 72 } } { 9 }$ 
C)  $y = \frac { 8 \sqrt { 81 - x ^ { 2 } } } { 9 }$ and $y = - \frac { 8 \sqrt { 81 - x ^ { 2 } } } { 9 }$ 
D)  $y = \frac { 8 \sqrt { 729 - x ^ { 2 } } } { 9 }$ and $y = - \frac { 8 \sqrt { 729 - x ^ { 2 } } } { 9 }$ 
A)  $y = \frac { 8 \sqrt { 9 - x ^ { 2 } } } { 9 }$ and $y = - \frac { 8 \sqrt { 9 - x ^ { 2 } } } { 9 }$ 
B)  $y = \frac { 8 \sqrt { - x ^ { 2 } + 6 x + 72 } } { 9 }$ and $y = - \frac { 8 \sqrt { - x ^ { 2 } + 6 x + 72 } } { 9 }$ 
C)  $y = \frac { 8 \sqrt { 81 - x ^ { 2 } } } { 9 }$ and $y = - \frac { 8 \sqrt { 81 - x ^ { 2 } } } { 9 }$ 
D)  $y = \frac { 8 \sqrt { 729 - x ^ { 2 } } } { 9 }$ and $y = - \frac { 8 \sqrt { 729 - x ^ { 2 } } } { 9 }$

Write the word or phrase that best completes each statement or answers the question. - $9 x ^ { 2 } + 49 y ^ { 2 } = 11,025$

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x - 2 = ( y - 8 ) ^ { 2 }$

Identify the type of graph. - $- x ^ { 2 } - 2 x + 4 y ^ { 2 } + 8 y = 20$

Give the focus, directrix, and axis for the parabola. - $x = 9 y ^ { 2 }$

Give the focus, directrix, and axis for the parabola. - $( y + 3 ) ^ { 2 } = 4 ( x + 2 )$

Find the eccentricity of the hyperbola. - $x ^ { 2 } - 25 y ^ { 2 } = 25$

Give the focus, directrix, and axis for the parabola. - $( y - 5 ) ^ { 2 } = - 12 ( x + 2 )$

Solve the problem. -An elliptical riding path is to be built on a rectangular piece of property that measures 10 mi by 4 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 Sides

Write the word or phrase that best completes each statement or answers the question. - $\frac { x ^ { 2 } } { 16 } = 1 - \frac { y ^ { 2 } } { 36 }$

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

Graph the ellipse. - $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 49 } = 1$ $Graph the ellipse. - \frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 49 } = 1$

Identify the type of graph. - $\frac { ( x - 7 ) ^ { 2 } } { 4 } + \frac { ( y - 6 ) ^ { 2 } } { 9 } = 0$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $y ^ { 2 } = 144 - x ^ { 2 }$

Graph the parabola. -

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $4 x = 3 y ^ { 2 } - 31$

Match the equation of the parabola with the appropriate description. - $x = 2 y ^ { 2 } - 6 y + 2$

Solve the problem. -A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is 18 ft and the vertical clearance must be 12 ft at a point 5 ft from the center. Find an equation for the ellipse.

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $16 x ^ { 2 } + 9 y ^ { 2 } = 144$

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { ( x - 3 ) ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 64 } = 1$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 10: Analytic Geometry

Write the word or phrase that best completes each statement or answers the question. - 9x2+49y2=11,0259 x ^ { 2 } + 49 y ^ { 2 } = 11,0259x2+49y2=11,025

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - x−2=(y−8)2x - 2 = ( y - 8 ) ^ { 2 }x−2=(y−8)2

Identify the type of graph. - −x2−2x+4y2+8y=20- x ^ { 2 } - 2 x + 4 y ^ { 2 } + 8 y = 20−x2−2x+4y2+8y=20

Give the focus, directrix, and axis for the parabola. - x=9y2x = 9 y ^ { 2 }x=9y2

Give the focus, directrix, and axis for the parabola. - (y+3)2=4(x+2)( y + 3 ) ^ { 2 } = 4 ( x + 2 )(y+3)2=4(x+2)

Find the eccentricity of the hyperbola. - x2−25y2=25x ^ { 2 } - 25 y ^ { 2 } = 25x2−25y2=25

Give the focus, directrix, and axis for the parabola. - (y−5)2=−12(x+2)( y - 5 ) ^ { 2 } = - 12 ( x + 2 )(y−5)2=−12(x+2)

Solve the problem. -An elliptical riding path is to be built on a rectangular piece of property that measures 10 mi by 4 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 Sides

Write the word or phrase that best completes each statement or answers the question. - x216=1−y236\frac { x ^ { 2 } } { 16 } = 1 - \frac { y ^ { 2 } } { 36 }16x2​=1−36y2​

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

Graph the ellipse. - x236+y249=1\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 49 } = 136x2​+49y2​=1

Identify the type of graph. - (x−7)24+(y−6)29=0\frac { ( x - 7 ) ^ { 2 } } { 4 } + \frac { ( y - 6 ) ^ { 2 } } { 9 } = 04(x−7)2​+9(y−6)2​=0

Identify the equation as a parabola, circle, ellipse, or hyperbola. - y2=144−x2y ^ { 2 } = 144 - x ^ { 2 }y2=144−x2

Graph the parabola. -

Identify the equation as a parabola, circle, ellipse, or hyperbola. - 4x=3y2−314 x = 3 y ^ { 2 } - 314x=3y2−31

Match the equation of the parabola with the appropriate description. - x=2y2−6y+2x = 2 y ^ { 2 } - 6 y + 2x=2y2−6y+2

Solve the problem. -A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is 18 ft and the vertical clearance must be 12 ft at a point 5 ft from the center. Find an equation for the ellipse.

Identify the equation as a parabola, circle, ellipse, or hyperbola. - 16x2+9y2=14416 x ^ { 2 } + 9 y ^ { 2 } = 14416x2+9y2=144

Determine the two equations necessary to graph the ellipse with a graphing calculator. - (x−3)281+y264=1\frac { ( x - 3 ) ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 64 } = 181(x−3)2​+64y2​=1

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Further Topics in Algebra

Review of Basic Concepts

Filters

Write the word or phrase that best completes each statement or answers the question. - $9 x ^ { 2 } + 49 y ^ { 2 } = 11,025$

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x - 2 = ( y - 8 ) ^ { 2 }$

Identify the type of graph. - $- x ^ { 2 } - 2 x + 4 y ^ { 2 } + 8 y = 20$

Give the focus, directrix, and axis for the parabola. - $x = 9 y ^ { 2 }$

Give the focus, directrix, and axis for the parabola. - $( y + 3 ) ^ { 2 } = 4 ( x + 2 )$

Find the eccentricity of the hyperbola. - $x ^ { 2 } - 25 y ^ { 2 } = 25$

Give the focus, directrix, and axis for the parabola. - $( y - 5 ) ^ { 2 } = - 12 ( x + 2 )$

Write the word or phrase that best completes each statement or answers the question. - $\frac { x ^ { 2 } } { 16 } = 1 - \frac { y ^ { 2 } } { 36 }$

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

Graph the ellipse. - $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 49 } = 1$ $Graph the ellipse. - \frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 49 } = 1$

Identify the type of graph. - $\frac { ( x - 7 ) ^ { 2 } } { 4 } + \frac { ( y - 6 ) ^ { 2 } } { 9 } = 0$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $y ^ { 2 } = 144 - x ^ { 2 }$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $4 x = 3 y ^ { 2 } - 31$

Match the equation of the parabola with the appropriate description. - $x = 2 y ^ { 2 } - 6 y + 2$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $16 x ^ { 2 } + 9 y ^ { 2 } = 144$

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { ( x - 3 ) ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 64 } = 1$