Question 1

The line segment with endpoints at the vertices of an ellipse is called the ________axis.

Accepted Answer

The answer of The line segment with endpoints at the...

Question 2

Solve the problem.
-A park has an elliptical shape with a major axis of 970 feet and a minor axis of 917 feet. Find the equation of the elliptical boundary.
a. Take the horizontal axis to be the major axis and locate the origin of the coordinate system at the
Center of the ellipse.
b. Approximate the eccentricity of the ellipse. Round to two decimal places.

Accepted Answer

A)  a. $\frac { x ^ { 2 } } { 485 ^ { 2 } } + \frac { y ^ { 2 } } { 458.5 ^ { 2 } } = 1$
b. $e \approx 0.11$ 
B)  $\mathbf { a } \cdot \frac { x ^ { 2 } } { 485 ^ { 2 } } + \frac { y ^ { 2 } } { 458.5 ^ { 2 } } = 1$
b. $e \approx 0.33$ 
C)  a. $\frac { x ^ { 2 } } { 970 ^ { 2 } } + \frac { y ^ { 2 } } { 917 ^ { 2 } } = 1$
b. $e \approx 0.33$ 
D)  a. $\frac { x ^ { 2 } } { 485 ^ { 2 } } + \frac { y ^ { 2 } } { 458.5 ^ { 2 } } = 1$
b. $e \approx 0.34$ 
A)  a. $\frac { x ^ { 2 } } { 485 ^ { 2 } } + \frac { y ^ { 2 } } { 458.5 ^ { 2 } } = 1$
b. $e \approx 0.11$ 
B)  $\mathbf { a } \cdot \frac { x ^ { 2 } } { 485 ^ { 2 } } + \frac { y ^ { 2 } } { 458.5 ^ { 2 } } = 1$
b. $e \approx 0.33$ 
C)  a. $\frac { x ^ { 2 } } { 970 ^ { 2 } } + \frac { y ^ { 2 } } { 917 ^ { 2 } } = 1$
b. $e \approx 0.33$ 
D)  a. $\frac { x ^ { 2 } } { 485 ^ { 2 } } + \frac { y ^ { 2 } } { 458.5 ^ { 2 } } = 1$
b. $e \approx 0.34$

Question 3

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The line perpendicular to the directrix and passing through the focus is called the axis of________ .

Accepted Answer

The answer of Write the word or phrase that best...

Question 4

Given $\frac { ( x - h ) ^ { 2 } } { a ^ { 2 } } + \frac { ( y - k ) ^ { 2 } } { b ^ { 2 } } = 1$ where $a > b > 0$ > 0, the ordered pairs representing the endpoints of the
vertices are ________and________ . The ordered pairs representing the endpoints of the minor axisare________ and________ .

Accepted Answer

The answer of Given \(\frac { ( x - h...

Question 5

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

Accepted Answer

A)  center: $( 6,7 )$;
vertices $( - 7,0 ) , ( 7,0 )$
  
B)  center: $( 0,0 )$;
vertices $( 0 , - 7 ) , ( 0,7 )$
  
C)  center: $( 6,7 )$;
vertices $( 0 , - 7 ) , ( 0,7 )$
  
D)  center: $( 0,0 )$;
vertices $( 0 , - 7 ) , ( 0,7 )$
  
A)  center: $( 6,7 )$;
vertices $( - 7,0 ) , ( 7,0 )$
  
B)  center: $( 0,0 )$;
vertices $( 0 , - 7 ) , ( 0,7 )$
  
C)  center: $( 6,7 )$;
vertices $( 0 , - 7 ) , ( 0,7 )$
  
D)  center: $( 0,0 )$;
vertices $( 0 , - 7 ) , ( 0,7 )$

Question 6

Given $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ where $a > b > 0$ e ordered pairs representing the vertices are________ and________. The ordered pairs representing the endpoints of the minor axis are ________and________
.

Accepted Answer

The answer of Given \(\frac { x ^ { 2...

Question 7

Identify the vertices and the foci, and write equations for the asymptotes.
-$\frac { 49 x ^ { 2 } } { 36 } - \frac { 49 y ^ { 2 } } { 64 } = 1$

Accepted Answer

A)  vertices: $\left( \frac { 7 } { 6 } , 0 \right) , \left( - \frac { 7 } { 6 } , 0 \right)$
foci: $\left( \frac { 10 } { 7 } , 0 \right) , \left( - \frac { 10 } { 7 } , 0 \right)$
asymptotes: $y = \frac { 3 } { 4 } x$ and $y = - \frac { 3 } { 4 } x$ 
B)  vertices: $\left( \frac { 7 } { 6 } , 0 \right) , \left( - \frac { 7 } { 6 } , 0 \right)$
foci: $\left( \frac { 10 } { 7 } , 0 \right) , \left( - \frac { 10 } { 7 } , 0 \right)$
asymptotes: $y = \frac { 4 } { 3 } x$ and $y = - \frac { 4 } { 3 } x$ 
C)  vertices: $\left( \frac { 7 } { 6 } , 0 \right) , \left( - \frac { 7 } { 6 } , 0 \right)$
foci: $\left( \frac { 70 } { 2,401 } , 0 \right) , \left( - \frac { 70 } { 2,401 } , 0 \right)$
asymptotes: $y = \frac { 4 } { 3 } x$ and $y = - \frac { 4 } { 3 } x$ 
D)  vertices: $\left( \frac { 7 } { 8 } , 0 \right) , \left( - \frac { 7 } { 8 } , 0 \right)$
foci: $\left. \left( \frac { 10 } { 7 } , 0 \right) , - \frac { 10 } { 7 } , 0 \right)$
 asymptotes: $y = \frac { 4 } { 3 } x$ and $y = - \frac { 4 } { 3 } x$ 
A)  vertices: $\left( \frac { 7 } { 6 } , 0 \right) , \left( - \frac { 7 } { 6 } , 0 \right)$
foci: $\left( \frac { 10 } { 7 } , 0 \right) , \left( - \frac { 10 } { 7 } , 0 \right)$
asymptotes: $y = \frac { 3 } { 4 } x$ and $y = - \frac { 3 } { 4 } x$ 
B)  vertices: $\left( \frac { 7 } { 6 } , 0 \right) , \left( - \frac { 7 } { 6 } , 0 \right)$
foci: $\left( \frac { 10 } { 7 } , 0 \right) , \left( - \frac { 10 } { 7 } , 0 \right)$
asymptotes: $y = \frac { 4 } { 3 } x$ and $y = - \frac { 4 } { 3 } x$ 
C)  vertices: $\left( \frac { 7 } { 6 } , 0 \right) , \left( - \frac { 7 } { 6 } , 0 \right)$
foci: $\left( \frac { 70 } { 2,401 } , 0 \right) , \left( - \frac { 70 } { 2,401 } , 0 \right)$
asymptotes: $y = \frac { 4 } { 3 } x$ and $y = - \frac { 4 } { 3 } x$ 
D)  vertices: $\left( \frac { 7 } { 8 } , 0 \right) , \left( - \frac { 7 } { 8 } , 0 \right)$
foci: $\left. \left( \frac { 10 } { 7 } , 0 \right) , - \frac { 10 } { 7 } , 0 \right)$
 asymptotes: $y = \frac { 4 } { 3 } x$ and $y = - \frac { 4 } { 3 } x$

Question 8

Write the standard form of an equation of the ellipse subject to the given conditions.
-Vertices: $( - 10,0 ) , ( 10,0 )$
Foci: $( - 6,0 ) , ( 6,0 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 100 } = 1$ 
B)  $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 64 } = 1$ 
C)  $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 36 } = 1$ 
D)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 100 } = 1$ 
A)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 100 } = 1$ 
B)  $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 64 } = 1$ 
C)  $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 36 } = 1$ 
D)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 100 } = 1$

Question 9

Determine the eccentricity of the hyperbola.
-$$\frac { ( x - 4 ) ^ { 2 } } { 144 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$$

Accepted Answer

A)  $e = \frac { 13 } { 5 }$ 
B)  $e = 2$ 
C)  $e = \frac { 12 } { 5 }$ 
D)  $e = \frac { 13 } { 12 }$ 
A)  $e = \frac { 13 } { 5 }$ 
B)  $e = 2$ 
C)  $e = \frac { 12 } { 5 }$ 
D)  $e = \frac { 13 } { 12 }$

Question 10

Write the equation of the ellipse in standard form. Identify the vertices and foci.
-$$36 x ^ { 2 } + 25 y ^ { 2 } + 100 y + 99 = 0$$

Accepted Answer

A)  $\frac { x ^ { 2 } } { \frac { 1 } { 36 } } + \frac { ( y + 2 ) ^ { 2 } } { \frac { 1 } { 25 } } = 1$
vertices: $\left( - \frac { 9 } { 5 } , 0 \right) , \left( - \frac { 11 } { 5 } , 0 \right)$
foci: $\left( 2 + \frac { \sqrt { 11 } } { 30 } , 0 \right) , \left( 2 - \frac { \sqrt { 11 } } { 30 } , 0 \right)$ 
B)  $\frac { x ^ { 2 } } { \frac { 1 } { 36 } } + \frac { ( y + 2 ) ^ { 2 } } { \frac { 1 } { 25 } } = 1$
vertices: $\left( 0 , - \frac { 9 } { 5 } \right) , \left( 0 , - \frac { 11 } { 5 } \right)$
foci: $\left( 0,2 + \frac { \sqrt { 11 } } { 30 } \right) , \left( 0,2 - \frac { \sqrt { 11 } } { 30 } \right)$ 
C)  $36 x ^ { 2 } + 25 ( y + 2 ) ^ { 2 } = 1$
vertices: $( 36 , - 2 ) , ( - 36 , - 2 )$
foci: $\left( 0,2 + \frac { \sqrt { 11 } } { 30 } \right) , \left( 0,2 - \frac { \sqrt { 11 } } { 30 } \right)$ 
D)  $36 x ^ { 2 } + 25 ( y + 2 ) ^ { 2 } = 1$
vertices: $\left( 0 , - \frac { 9 } { 5 } \right) , \left( 0 , - \frac { 11 } { 5 } \right)$
foci: $\left( 0,2 + \frac { \sqrt { 11 } } { 30 } \right) , \left( 0,2 - \frac { \sqrt { 11 } } { 30 } \right)$ 
A)  $\frac { x ^ { 2 } } { \frac { 1 } { 36 } } + \frac { ( y + 2 ) ^ { 2 } } { \frac { 1 } { 25 } } = 1$
vertices: $\left( - \frac { 9 } { 5 } , 0 \right) , \left( - \frac { 11 } { 5 } , 0 \right)$
foci: $\left( 2 + \frac { \sqrt { 11 } } { 30 } , 0 \right) , \left( 2 - \frac { \sqrt { 11 } } { 30 } , 0 \right)$ 
B)  $\frac { x ^ { 2 } } { \frac { 1 } { 36 } } + \frac { ( y + 2 ) ^ { 2 } } { \frac { 1 } { 25 } } = 1$
vertices: $\left( 0 , - \frac { 9 } { 5 } \right) , \left( 0 , - \frac { 11 } { 5 } \right)$
foci: $\left( 0,2 + \frac { \sqrt { 11 } } { 30 } \right) , \left( 0,2 - \frac { \sqrt { 11 } } { 30 } \right)$ 
C)  $36 x ^ { 2 } + 25 ( y + 2 ) ^ { 2 } = 1$
vertices: $( 36 , - 2 ) , ( - 36 , - 2 )$
foci: $\left( 0,2 + \frac { \sqrt { 11 } } { 30 } \right) , \left( 0,2 - \frac { \sqrt { 11 } } { 30 } \right)$ 
D)  $36 x ^ { 2 } + 25 ( y + 2 ) ^ { 2 } = 1$
vertices: $\left( 0 , - \frac { 9 } { 5 } \right) , \left( 0 , - \frac { 11 } { 5 } \right)$
foci: $\left( 0,2 + \frac { \sqrt { 11 } } { 30 } \right) , \left( 0,2 - \frac { \sqrt { 11 } } { 30 } \right)$

Question 11

Write the standard form of an equation of the ellipse subject to the given conditions.
-Foci: $( - 5,5 )$ and $( 3,5 )$
Length of minor axis: 4

Accepted Answer

A)  $\frac { ( x + 1 ) ^ { 2 } } { 20 } + \frac { ( y - 5 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y - 5 ) ^ { 2 } } { 20 } = 1$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { 4 } + \frac { ( y + 1 ) ^ { 2 } } { 20 } = 1$ 
D)  $\frac { ( x - 5 ) ^ { 2 } } { 20 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$ 
A)  $\frac { ( x + 1 ) ^ { 2 } } { 20 } + \frac { ( y - 5 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y - 5 ) ^ { 2 } } { 20 } = 1$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { 4 } + \frac { ( y + 1 ) ^ { 2 } } { 20 } = 1$ 
D)  $\frac { ( x - 5 ) ^ { 2 } } { 20 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$

Question 12

Fill in the blanks. Le $| \boldsymbol { p } |$ | represent the focal length (the distance between the vertex and the focus).
-If the vertex of a parabola is (-2, -4) and the focus is (-4, -4), then the directrix is given by the equation ________ and the value of p is ________.

Accepted Answer

A)  x = -4; -2 
B)  x = 0; -4 
C)  x = 0; -2 
D)  y = 0; -2 
A)  x = -4; -2 
B)  x = 0; -4 
C)  x = 0; -2 
D)  y = 0; -2

Question 13

Determine the standard form of an equation of the parabola subject to the given conditions.
-Vertex: $( 0,0 )$; Directrix: $y = - 8$

Accepted Answer

A)  $x ^ { 2 } = 32 y$ 
B)  $y ^ { 2 } = 32 x$ 
C)  $y ^ { 2 } = - 8 x$ 
D)  $x ^ { 2 } = - 8 y$ 
A)  $x ^ { 2 } = 32 y$ 
B)  $y ^ { 2 } = 32 x$ 
C)  $y ^ { 2 } = - 8 x$ 
D)  $x ^ { 2 } = - 8 y$

Question 14

Identify the vertices and the foci.
-$$x ^ { 2 } - \frac { ( y + 5 ) ^ { 2 } } { 3 } = 1$$

Accepted Answer

A)  vertices: $( 1,5 ) , ( - 1,5 )$
foci: $( 2,5 ) , ( - 2,5 )$ 
B)  vertices: $( 1 , - 5 ) , ( - 1 , - 5 )$
foci: $( 2 , - 5 ) , ( - 2 , - 5 )$ 
C)  vertices: $( 0 , - 5 + \sqrt { 3 } ) , ( 0 , - 5 - \sqrt { 3 } )$
foci: $( 0 , - 7 ) , ( 0 , - 3 )$ 
D)  vertices: $( 0,5 + \sqrt { 3 } ) , ( 0,5 - \sqrt { 3 } )$
foci: $( 0,7 ) , ( 0,3 )$ 
A)  vertices: $( 1,5 ) , ( - 1,5 )$
foci: $( 2,5 ) , ( - 2,5 )$ 
B)  vertices: $( 1 , - 5 ) , ( - 1 , - 5 )$
foci: $( 2 , - 5 ) , ( - 2 , - 5 )$ 
C)  vertices: $( 0 , - 5 + \sqrt { 3 } ) , ( 0 , - 5 - \sqrt { 3 } )$
foci: $( 0 , - 7 ) , ( 0 , - 3 )$ 
D)  vertices: $( 0,5 + \sqrt { 3 } ) , ( 0,5 - \sqrt { 3 } )$
foci: $( 0,7 ) , ( 0,3 )$

Question 15

Determine the length of the major and minor axis.
-$$4 x ^ { 2 } + 81 y ^ { 2 } = 324$$

Accepted Answer

A)  length of major axis: 18 ;
 length of minor axis: 4 
B)  length of major axis: 81 ;
length of minor axis: 4 
C)  length of major axis: 2 ;
length of minor axis: 9 
D)  length of major axis: 9 ; 
 length of minor axis: 2 
A)  length of major axis: 18 ;
 length of minor axis: 4 
B)  length of major axis: 81 ;
length of minor axis: 4 
C)  length of major axis: 2 ;
length of minor axis: 9 
D)  length of major axis: 9 ; 
 length of minor axis: 2

Question 16

Solve the problem.
-Suppose a solar cooker has a parabolic mirror (see figure).  
$$14 \mathrm { in } .$$ a. Use a coordinate system with the origin at the vertex of the mirror and write an equation of a parabolic cross section of the mirror.
b. Where should a pot be placed so it receives maximum heat?

Accepted Answer

A)  a. $x ^ { 2 } = 14 y$ for $- 14 \leq x \leq 14$
b. The pot should be placed $3.5 \mathrm { in }$. above the vertex 
B)  a. $x ^ { 2 } = 28 y$ for $- 14 \leq x \leq 14$
b. The pot should be placed 28 in. above the vertex 
C)  a. $x ^ { 2 } = 14 y$ for $- 14 \leq x \leq 14$
b. The pot should be placed $14 \mathrm { in }$. above the vertex 
D)  a. $x ^ { 2 } = 28 y$ for $- 14 \leq x \leq 14$
b. The pot should be placed 7 in. above the vertex 
A)  a. $x ^ { 2 } = 14 y$ for $- 14 \leq x \leq 14$
b. The pot should be placed $3.5 \mathrm { in }$. above the vertex 
B)  a. $x ^ { 2 } = 28 y$ for $- 14 \leq x \leq 14$
b. The pot should be placed 28 in. above the vertex 
C)  a. $x ^ { 2 } = 14 y$ for $- 14 \leq x \leq 14$
b. The pot should be placed $14 \mathrm { in }$. above the vertex 
D)  a. $x ^ { 2 } = 28 y$ for $- 14 \leq x \leq 14$
b. The pot should be placed 7 in. above the vertex

Question 17

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The distance between the vertex and the focus of a parabola is called the ________length and is often represented by $$| p |$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 18

Write the equation of the hyperbola in standard form. Identify the center and vertices.
-$$4 y ^ { 2 } - 16 x ^ { 2 } + 40 y - 32 x + 20 = 0$$

Accepted Answer

A)  $\frac { ( y - 5 ) ^ { 2 } } { 16 } - \frac { ( x - 1 ) ^ { 2 } } { 4 } = 1$
center: $( - 1 , - 5 )$; vertices: $( - 1 , - 9 ) , ( - 1 , - 1 )$ 
B)  $\frac { ( y + 5 ) ^ { 2 } } { 16 } - \frac { ( x + 1 ) ^ { 2 } } { 4 } = 1$
center: $( - 1 , - 5 )$; vertices: $( - 1 , - 9 ) , ( - 1 , - 1 )$ 
C)  $\frac { ( y + 5 ) ^ { 2 } } { 16 } - \frac { ( x + 1 ) ^ { 2 } } { 4 } = 1$
center: $( 1,5 )$; vertices: $( 1,1 ) , ( 1,9 )$ 
D)  $\frac { ( y - 5 ) ^ { 2 } } { 16 } - \frac { ( x - 1 ) ^ { 2 } } { 4 } = 1$
center: $( 1,5 )$; vertices: $( 1,1 ) , ( 1,9 )$ 
A)  $\frac { ( y - 5 ) ^ { 2 } } { 16 } - \frac { ( x - 1 ) ^ { 2 } } { 4 } = 1$
center: $( - 1 , - 5 )$; vertices: $( - 1 , - 9 ) , ( - 1 , - 1 )$ 
B)  $\frac { ( y + 5 ) ^ { 2 } } { 16 } - \frac { ( x + 1 ) ^ { 2 } } { 4 } = 1$
center: $( - 1 , - 5 )$; vertices: $( - 1 , - 9 ) , ( - 1 , - 1 )$ 
C)  $\frac { ( y + 5 ) ^ { 2 } } { 16 } - \frac { ( x + 1 ) ^ { 2 } } { 4 } = 1$
center: $( 1,5 )$; vertices: $( 1,1 ) , ( 1,9 )$ 
D)  $\frac { ( y - 5 ) ^ { 2 } } { 16 } - \frac { ( x - 1 ) ^ { 2 } } { 4 } = 1$
center: $( 1,5 )$; vertices: $( 1,1 ) , ( 1,9 )$

Question 19

Fill in the blanks. Le $| \boldsymbol { p } |$ | represent the focal length (the distance between the vertex and the focus).
-If the focal diameter of a parabola is 8 units, then the focal length is ________ units.

Accepted Answer

A)  2 
B)  4 
C)  -2 
D)  32 
A)  2 
B)  4 
C)  -2 
D)  32

Question 20

Solve the system of equations.
-$$\begin{array} { l } 
\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 49 } = 1 \
- 7 x + 9 y = - 63
\end{array}$$

Accepted Answer

A)  $\{ ( - 7,0 ) , ( 0,9 ) \}$ 
B)  $\{ ( 0,7 ) , ( - 9,0 ) \}$ 
C)  $\{ ( 7,0 ) , ( 0 , - 9 ) \}$ 
D)  $\{ ( 0 , - 7 ) , ( 9,0 ) \}$ 
A)  $\{ ( - 7,0 ) , ( 0,9 ) \}$ 
B)  $\{ ( 0,7 ) , ( - 9,0 ) \}$ 
C)  $\{ ( 7,0 ) , ( 0 , - 9 ) \}$ 
D)  $\{ ( 0 , - 7 ) , ( 9,0 ) \}$

The line segment with endpoints at the vertices of an ellipse is called the ________axis.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The line perpendicular to the directrix and passing through the focus is called the axis of________ .

Given $\frac { ( x - h ) ^ { 2 } } { a ^ { 2 } } + \frac { ( y - k ) ^ { 2 } } { b ^ { 2 } } = 1$ where $a > b > 0$ > 0, the ordered pairs representing the endpoints of the vertices are and . The ordered pairs representing the endpoints of the minor axisare and .

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

Given $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ where $a > b > 0$ e ordered pairs representing the vertices are and. The ordered pairs representing the endpoints of the minor axis are and .

Identify the vertices and the foci, and write equations for the asymptotes. - $\frac { 49 x ^ { 2 } } { 36 } - \frac { 49 y ^ { 2 } } { 64 } = 1$

Write the standard form of an equation of the ellipse subject to the given conditions. -Vertices: $( - 10,0 ) , ( 10,0 )$ Foci: $( - 6,0 ) , ( 6,0 )$

Determine the eccentricity of the hyperbola. - $\frac { ( x - 4 ) ^ { 2 } } { 144 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$

Write the equation of the ellipse in standard form. Identify the vertices and foci. - $36 x ^ { 2 } + 25 y ^ { 2 } + 100 y + 99 = 0$

Write the standard form of an equation of the ellipse subject to the given conditions. -Foci: $( - 5,5 )$ and $( 3,5 )$ Length of minor axis: 4

Fill in the blanks. Le $| \boldsymbol { p } |$ | represent the focal length (the distance between the vertex and the focus). -If the vertex of a parabola is (-2, -4) and the focus is (-4, -4), then the directrix is given by the equation and the value of p is .

Determine the standard form of an equation of the parabola subject to the given conditions. -Vertex: $( 0,0 )$ ; Directrix: $y = - 8$

Identify the vertices and the foci. - $x ^ { 2 } - \frac { ( y + 5 ) ^ { 2 } } { 3 } = 1$

Determine the length of the major and minor axis. - $4 x ^ { 2 } + 81 y ^ { 2 } = 324$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The distance between the vertex and the focus of a parabola is called the ________length and is often represented by $| p |$

Write the equation of the hyperbola in standard form. Identify the center and vertices. - $4 y ^ { 2 } - 16 x ^ { 2 } + 40 y - 32 x + 20 = 0$

Fill in the blanks. Le $| \boldsymbol { p } |$ | represent the focal length (the distance between the vertex and the focus). -If the focal diameter of a parabola is 8 units, then the focal length is ________ units.

Solve the system of equations. - +=1 -7x+9y=-63

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

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Exam 7: Analytic Geometry

The line segment with endpoints at the vertices of an ellipse is called the ________axis.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The line perpendicular to the directrix and passing through the focus is called the axis of________ .

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

Given x2a2+y2b2=1\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1a2x2​+b2y2​=1 where a>b>0a > b > 0a>b>0 e ordered pairs representing the vertices are________ and________. The ordered pairs representing the endpoints of the minor axis are ________and________ .

Identify the vertices and the foci, and write equations for the asymptotes. - 49x236−49y264=1\frac { 49 x ^ { 2 } } { 36 } - \frac { 49 y ^ { 2 } } { 64 } = 13649x2​−6449y2​=1

Write the standard form of an equation of the ellipse subject to the given conditions. -Vertices: (−10,0),(10,0)( - 10,0 ) , ( 10,0 )(−10,0),(10,0) Foci: (−6,0),(6,0)( - 6,0 ) , ( 6,0 )(−6,0),(6,0)

Determine the eccentricity of the hyperbola. - (x−4)2144−(y+2)225=1\frac { ( x - 4 ) ^ { 2 } } { 144 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1144(x−4)2​−25(y+2)2​=1

Write the equation of the ellipse in standard form. Identify the vertices and foci. - 36x2+25y2+100y+99=036 x ^ { 2 } + 25 y ^ { 2 } + 100 y + 99 = 036x2+25y2+100y+99=0

Write the standard form of an equation of the ellipse subject to the given conditions. -Foci: (−5,5)( - 5,5 )(−5,5) and (3,5)( 3,5 )(3,5) Length of minor axis: 4

Fill in the blanks. Le ∣p∣| \boldsymbol { p } |∣p∣ | represent the focal length (the distance between the vertex and the focus). -If the vertex of a parabola is (-2, -4) and the focus is (-4, -4), then the directrix is given by the equation ________ and the value of p is ________.

Determine the standard form of an equation of the parabola subject to the given conditions. -Vertex: (0,0)( 0,0 )(0,0) ; Directrix: y=−8y = - 8y=−8

Identify the vertices and the foci. - x2−(y+5)23=1x ^ { 2 } - \frac { ( y + 5 ) ^ { 2 } } { 3 } = 1x2−3(y+5)2​=1

Determine the length of the major and minor axis. - 4x2+81y2=3244 x ^ { 2 } + 81 y ^ { 2 } = 3244x2+81y2=324

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The distance between the vertex and the focus of a parabola is called the ________length and is often represented by ∣p∣| p |∣p∣

Write the equation of the hyperbola in standard form. Identify the center and vertices. - 4y2−16x2+40y−32x+20=04 y ^ { 2 } - 16 x ^ { 2 } + 40 y - 32 x + 20 = 04y2−16x2+40y−32x+20=0

Fill in the blanks. Le ∣p∣| \boldsymbol { p } |∣p∣ | represent the focal length (the distance between the vertex and the focus). -If the focal diameter of a parabola is 8 units, then the focal length is ________ units.

Solve the system of equations. - +=1 -7x+9y=-63

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

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

Given $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ where $a > b > 0$ e ordered pairs representing the vertices are and. The ordered pairs representing the endpoints of the minor axis are and .

Identify the vertices and the foci, and write equations for the asymptotes. - $\frac { 49 x ^ { 2 } } { 36 } - \frac { 49 y ^ { 2 } } { 64 } = 1$

Write the standard form of an equation of the ellipse subject to the given conditions. -Vertices: $( - 10,0 ) , ( 10,0 )$ Foci: $( - 6,0 ) , ( 6,0 )$

Determine the eccentricity of the hyperbola. - $\frac { ( x - 4 ) ^ { 2 } } { 144 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$

Write the equation of the ellipse in standard form. Identify the vertices and foci. - $36 x ^ { 2 } + 25 y ^ { 2 } + 100 y + 99 = 0$

Write the standard form of an equation of the ellipse subject to the given conditions. -Foci: $( - 5,5 )$ and $( 3,5 )$ Length of minor axis: 4

Fill in the blanks. Le $| \boldsymbol { p } |$ | represent the focal length (the distance between the vertex and the focus). -If the vertex of a parabola is (-2, -4) and the focus is (-4, -4), then the directrix is given by the equation and the value of p is .

Determine the standard form of an equation of the parabola subject to the given conditions. -Vertex: $( 0,0 )$ ; Directrix: $y = - 8$

Identify the vertices and the foci. - $x ^ { 2 } - \frac { ( y + 5 ) ^ { 2 } } { 3 } = 1$

Determine the length of the major and minor axis. - $4 x ^ { 2 } + 81 y ^ { 2 } = 324$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The distance between the vertex and the focus of a parabola is called the ________length and is often represented by $| p |$

Write the equation of the hyperbola in standard form. Identify the center and vertices. - $4 y ^ { 2 } - 16 x ^ { 2 } + 40 y - 32 x + 20 = 0$

Fill in the blanks. Le $| \boldsymbol { p } |$ | represent the focal length (the distance between the vertex and the focus). -If the focal diameter of a parabola is 8 units, then the focal length is ________ units.