Question 1

Determine the type of graph defined by $x ^ { 2 } + y ^ { 2 } = 92$ .

Accepted Answer

A)  parabola 
B)  ellipse 
C)  circle 
A)  parabola 
B)  ellipse 
C)  circle C

Question 2

Solve the system of equations algebraically for real values of x and y . $\left\{ \begin{array} { l } 
x y = \frac { 1 } { 6 } \
y + x = 5 x y
\end{array} \right.$

Accepted Answer

$\left( \frac { 1 } { 2 } , \frac { 1 } { 3 } \right) , \left( \frac { 1 } { 3 } , \frac { 1 } { 2 } \right)$

Question 3

Determine whether $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$ is a solution of the system $1 + \log _ { 4 } 9 x - \log _ { 4 } y$

Accepted Answer

no

Question 4

Solve the system of equations for real values of x and y . $\left\{ \begin{array} { l } 
y ^ { 2 } = 20 - x ^ { 2 } \
3 y = x ^ { 2 } - 16
\end{array} \right.$

Accepted Answer

The answer of Solve the system of equations for real...

Question 5

Graph the equation. $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Accepted Answer

The answer of Graph the equation. \(\log _ { 4...

Question 6

Graph: $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$

Accepted Answer

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

Question 7

Solve: $\left\{ \begin{aligned}
x y & = 8 \
3 x + y & = 14
\end{aligned} \right.$

Accepted Answer

The answer of Solve: \(\left\{ \begin{aligned}
x y & = 8...

Question 8

Write the equation $x ^ { 2 } - y ^ { 2 } - 2 x - 2 y = 25$ in standard form to show that it describes a hyperbola.

Accepted Answer

The answer of Write the equation \(x ^ { 2...

Question 9

Find the x -intercept(s) for $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 81 } = 1$

Accepted Answer

A)  $( 0,6 )$ , $( 0 , - 6 )$ 
B)  $( 9,0 )$ , $( - 9,0 )$ 
C)  $( 6,0 )$ , $( - 6,0 )$ 
D)  $( 0,9 )$ , $( 0 , - 9 )$ 
A)  $( 0,6 )$ , $( 0 , - 6 )$ 
B)  $( 9,0 )$ , $( - 9,0 )$ 
C)  $( 6,0 )$ , $( - 6,0 )$ 
D)  $( 0,9 )$ , $( 0 , - 9 )$

Question 10

The line segment joining the vertices of an ellipse is called the __________ of the ellipse.

Accepted Answer

The answer of The line segment joining the vertices of...

Question 11

Describe the hyperbola which is the graph of the equation $\frac { y ^ { 2 } } { 9 } - \frac { ( x + 4 ) ^ { 2 } } { 49 } = 1$ .

Accepted Answer

A)  center: $( 0 , - 4 )$ ; vertices: $( 0,3 )$ , $( 0 , - 3 )$ 
B)  center: $( - 4,0 )$ ; vertices: $( - 4,3 )$ , $( - 4 , - 3 )$ 
C)  center: $( 4,0 )$ ; vertices: $( 4,3 )$ , $( 4 , - 3 )$ 
D)  center: $( - 4,0 )$ ; vertices: $( 0,7 )$ , $( 0,4 )$ 
A)  center: $( 0 , - 4 )$ ; vertices: $( 0,3 )$ , $( 0 , - 3 )$ 
B)  center: $( - 4,0 )$ ; vertices: $( - 4,3 )$ , $( - 4 , - 3 )$ 
C)  center: $( 4,0 )$ ; vertices: $( 4,3 )$ , $( 4 , - 3 )$ 
D)  center: $( - 4,0 )$ ; vertices: $( 0,7 )$ , $( 0,4 )$

Question 12

Write $81 x ^ { 2 } + 25 y ^ { 2 } = 1$ in standard form of the equation of an ellipse. Give the values for a and b.

Accepted Answer

The answer of Write \(81 x ^ { 2 }...

Question 13

The midpoint of the major axis of an ellipse is the __________ of the ellipse.

Accepted Answer

The answer of The midpoint of the major axis of...

Question 14

Graph the equation. $\log _ { 7 } \frac { x y } { 7 }$

Accepted Answer

The answer of Graph the equation. \(\log _ { 7...

Question 15

The graph of the equation $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$ is a(n) _________.

Accepted Answer

The answer of The graph of the equation \(\frac {...

Question 16

Determine whether the equation, when graphed, will be a circle , a parabola , an ellipse , or a hyperbola . $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Accepted Answer

The answer of Determine whether the equation, when graphed, will...

Question 17

Find the center of the ellipse graphed below. What are a and b ?
   Center:_________ a = ______ b =______

Accepted Answer

Center: (0

Question 18

Graph: $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$

Accepted Answer

The answer of Graph: \(\frac { y ^ { 2...

Question 19

In the graph, $\log _ { 7 } \frac { x y } { 7 }$ and $\log _ { 7 } x + \log _ { 7 } y - 1$ are the __________ of the ellipse. Each one is called a(n) __________ of the ellipse. $\log _ { 7 } x - \log _ { 7 } y + 1$

Accepted Answer

The answer of In the graph, \(\log _ { 7...

Question 20

The extended diagonals of the central rectangle are _________ of the hyperbola.

Accepted Answer

The answer of The extended diagonals of the central rectangle...

Determine the type of graph defined by $x ^ { 2 } + y ^ { 2 } = 92$ .

Solve the system of equations algebraically for real values of x and y . $\left\{ \begin{array} { l } x y = \frac { 1 } { 6 } \\y + x = 5 x y\end{array} \right.$

Determine whether $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$ is a solution of the system $1 + \log _ { 4 } 9 x - \log _ { 4 } y$

Solve the system of equations for real values of x and y . $\left\{ \begin{array} { l } y ^ { 2 } = 20 - x ^ { 2 } \\3 y = x ^ { 2 } - 16\end{array} \right.$

Graph the equation. $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Graph: $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$

Solve: $\left\{ \begin{aligned}x y & = 8 \\3 x + y & = 14\end{aligned} \right.$

Write the equation $x ^ { 2 } - y ^ { 2 } - 2 x - 2 y = 25$ in standard form to show that it describes a hyperbola.

Find the x -intercept(s) for $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 81 } = 1$

The line segment joining the vertices of an ellipse is called the __________ of the ellipse.

Describe the hyperbola which is the graph of the equation $\frac { y ^ { 2 } } { 9 } - \frac { ( x + 4 ) ^ { 2 } } { 49 } = 1$ .

Write $81 x ^ { 2 } + 25 y ^ { 2 } = 1$ in standard form of the equation of an ellipse. Give the values for a and b.

The midpoint of the major axis of an ellipse is the __________ of the ellipse.

Graph the equation. $\log _ { 7 } \frac { x y } { 7 }$

The graph of the equation $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$ is a(n) _________.

Determine whether the equation, when graphed, will be a circle , a parabola , an ellipse , or a hyperbola . $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Find the center of the ellipse graphed below. What are a and b ? Center:_ a = b =

Graph: $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$

In the graph, $\log _ { 7 } \frac { x y } { 7 }$ and $\log _ { 7 } x + \log _ { 7 } y - 1$ are the of the ellipse. Each one is called a(n) of the ellipse. $\log _ { 7 } x - \log _ { 7 } y + 1$

The extended diagonals of the central rectangle are _________ of the hyperbola.

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Miscellaneous Topics

Filters

Exam 10: Conic Sections; More Graphing

Determine the type of graph defined by x2+y2=92x ^ { 2 } + y ^ { 2 } = 92x2+y2=92 .

Solve the system of equations algebraically for real values of x and y . {xy=16y+x=5xy\left\{ \begin{array} { l } x y = \frac { 1 } { 6 } \\y + x = 5 x y\end{array} \right.{xy=61​y+x=5xy​

Determine whether log⁡44x9y\log _ { 4 } \frac { 4 x ^ { 9 } } { y }log4​y4x9​ is a solution of the system 1+log⁡49x−log⁡4y1 + \log _ { 4 } 9 x - \log _ { 4 } y1+log4​9x−log4​y

Solve the system of equations for real values of x and y . {y2=20−x23y=x2−16\left\{ \begin{array} { l } y ^ { 2 } = 20 - x ^ { 2 } \\3 y = x ^ { 2 } - 16\end{array} \right.{y2=20−x23y=x2−16​

Graph the equation. log⁡44x9y\log _ { 4 } \frac { 4 x ^ { 9 } } { y }log4​y4x9​

Graph: x24+y225=1\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 14x2​+25y2​=1

Solve: {xy=83x+y=14\left\{ \begin{aligned}x y & = 8 \\3 x + y & = 14\end{aligned} \right.{xy3x+y​=8=14​

Write the equation x2−y2−2x−2y=25x ^ { 2 } - y ^ { 2 } - 2 x - 2 y = 25x2−y2−2x−2y=25 in standard form to show that it describes a hyperbola.

Find the x -intercept(s) for x236−y281=1\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 81 } = 136x2​−81y2​=1

The line segment joining the vertices of an ellipse is called the __________ of the ellipse.

Describe the hyperbola which is the graph of the equation y29−(x+4)249=1\frac { y ^ { 2 } } { 9 } - \frac { ( x + 4 ) ^ { 2 } } { 49 } = 19y2​−49(x+4)2​=1 .

Write 81x2+25y2=181 x ^ { 2 } + 25 y ^ { 2 } = 181x2+25y2=1 in standard form of the equation of an ellipse. Give the values for a and b.

The midpoint of the major axis of an ellipse is the __________ of the ellipse.

Graph the equation. log⁡7xy7\log _ { 7 } \frac { x y } { 7 }log7​7xy​

The graph of the equation x29+y216=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 19x2​+16y2​=1 is a(n) _________.

Determine whether the equation, when graphed, will be a circle , a parabola , an ellipse , or a hyperbola . log⁡44x9y\log _ { 4 } \frac { 4 x ^ { 9 } } { y }log4​y4x9​

Find the center of the ellipse graphed below. What are a and b ? Center:_________ a = ______ b =______

Graph: y29−x216=1\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 19y2​−16x2​=1

The extended diagonals of the central rectangle are _________ of the hyperbola.

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Miscellaneous Topics

Filters

Determine the type of graph defined by $x ^ { 2 } + y ^ { 2 } = 92$ .

Solve the system of equations algebraically for real values of x and y . $\left\{ \begin{array} { l } x y = \frac { 1 } { 6 } \\y + x = 5 x y\end{array} \right.$

Determine whether $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$ is a solution of the system $1 + \log _ { 4 } 9 x - \log _ { 4 } y$

Solve the system of equations for real values of x and y . $\left\{ \begin{array} { l } y ^ { 2 } = 20 - x ^ { 2 } \\3 y = x ^ { 2 } - 16\end{array} \right.$

Graph the equation. $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Graph: $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$

Solve: $\left\{ \begin{aligned}x y & = 8 \\3 x + y & = 14\end{aligned} \right.$

Write the equation $x ^ { 2 } - y ^ { 2 } - 2 x - 2 y = 25$ in standard form to show that it describes a hyperbola.

Find the x -intercept(s) for $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 81 } = 1$

Describe the hyperbola which is the graph of the equation $\frac { y ^ { 2 } } { 9 } - \frac { ( x + 4 ) ^ { 2 } } { 49 } = 1$ .

Write $81 x ^ { 2 } + 25 y ^ { 2 } = 1$ in standard form of the equation of an ellipse. Give the values for a and b.

Graph the equation. $\log _ { 7 } \frac { x y } { 7 }$

The graph of the equation $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$ is a(n) _________.

Determine whether the equation, when graphed, will be a circle , a parabola , an ellipse , or a hyperbola . $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Find the center of the ellipse graphed below. What are a and b ? Center:_ a = b =

Graph: $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$