Question 1

An equation of a parabola $$( x - h ) ^ { 2 } = 4 p ( y - k )$$ is given. Graph the parabola. Identify the vertex and the
focal diameter.
-$$( x + 3 ) ^ { 2 } = - 4 ( y + 4 )$$

Accepted Answer

A)  vertex: $( 3,4 )$; focal diameter: 4
  
B)  vertex: $( 3,4 )$; focal diameter: 1
  
C)  vertex: $( - 3 , - 4 )$; focal diameter: 4
  
D)  vertex: $( - 3 , - 4 )$; focal diameter: 1
  
A)  vertex: $( 3,4 )$; focal diameter: 4
  
B)  vertex: $( 3,4 )$; focal diameter: 1
  
C)  vertex: $( - 3 , - 4 )$; focal diameter: 4
  
D)  vertex: $( - 3 , - 4 )$; focal diameter: 1

Question 2

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the
vertex and the focal diameter.
-$$y ^ { 2 } - 8 y - 12 x - 8 = 0$$

Accepted Answer

A)  $( y - 4 ) ^ { 2 } = 12 ( x + 2 )$
vertex: $( - 2,4 )$; focal diameter: 12 
B)  $( y + 4 ) ^ { 2 } = 12 ( x - 2 )$
vertex: $( - 4,2 )$; focal diameter: 6 
C)  $( y - 4 ) ^ { 2 } = 12 ( x + 2 )$
vertex: $( - 2,4 )$; focal diameter: 6 
D)  $( y + 4 ) ^ { 2 } = 12 ( x - 2 )$
vertex: $( - 4,2 )$; focal diameter: 12 
A)  $( y - 4 ) ^ { 2 } = 12 ( x + 2 )$
vertex: $( - 2,4 )$; focal diameter: 12 
B)  $( y + 4 ) ^ { 2 } = 12 ( x - 2 )$
vertex: $( - 4,2 )$; focal diameter: 6 
C)  $( y - 4 ) ^ { 2 } = 12 ( x + 2 )$
vertex: $( - 2,4 )$; focal diameter: 6 
D)  $( y + 4 ) ^ { 2 } = 12 ( x - 2 )$
vertex: $( - 4,2 )$; focal diameter: 12

Question 3

Solve the problem.
- Radio signals emitted from points (10, 0) and (-10, 0) indicate that a plane is 8 miles closer to (10,0) than to (-10, 0). Find an equation of the hyperbola that passes through the plane's location with foci (10, 0) and (-10, 0). All units are in miles.
Radio signals emitted from points (0, 8) and (0, -8) indicate that a plane is 4 miles farther from (0, 8) than (0, -8). Find an equation of the hyperbola that passes through the plane's location with foci (0,8) and (0, -8).
From the figure, the plane is located in the fourth quadrant of the coordinate system. Solve the system of equations defining the two hyperbolas for the point of intersection in the fourth quadrant. This is the location o the plane. 
Round the coordinates to the nearest tenth of a mile.

Accepted Answer

A)  a. $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 84 } = 1$
b. $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 60 } = 1$
c. $( 4.1,2.3 )$ 
B)  $\mathrm { a } \cdot \frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 84 } = 1$
b. $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 60 } = 1$
c. $( 4.1 , - 2.3 )$ 
C)  a. $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 84 } = 1$
b. $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 60 } = 1$
c. $( - 2.3,4.1 )$ 
D)  a. $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 84 } = 1$
b. $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 60 } = 1$
c. $( 4.1 , - 2.3 )$ 
A)  a. $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 84 } = 1$
b. $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 60 } = 1$
c. $( 4.1,2.3 )$ 
B)  $\mathrm { a } \cdot \frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 84 } = 1$
b. $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 60 } = 1$
c. $( 4.1 , - 2.3 )$ 
C)  a. $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 84 } = 1$
b. $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 60 } = 1$
c. $( - 2.3,4.1 )$ 
D)  a. $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 84 } = 1$
b. $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 60 } = 1$
c. $( 4.1 , - 2.3 )$

Question 4

Solve the problem.
-a. A circular vent pipe with diameter 4 inches is placed on a flat roof. Write an equation of the circular cross section that the pipe makes with the roof. Assume the origin is placed at the center of The circle.
b. Suppose the pipe is instead placed on a roof with a slope of $\frac { 3 } { 4 }$ . The cross-section of the pipe Where it intersects the roof is an ellipse. Determine the lengths of the major and minor axes of this Ellipse.

Accepted Answer

A)  a. $x ^ { 2 } + y ^ { 2 } = 4$
b. Major axis $= 4$ in; minor axis $\approx 5.0$ in 
B)  a. $x ^ { 2 } + y ^ { 2 } = 16$
b. Major axis $\approx 2.5$ in; minor axis $= 2$ in 
C)  a. $x ^ { 2 } + y ^ { 2 } = 16$
b. Major axis $\approx 6.7$ in; minor axis $= 4$ in 
D)  a. $x ^ { 2 } + y ^ { 2 } = 4$
b. Major axis $\approx 5.0$ in; minor axis $= 4$ in 
A)  a. $x ^ { 2 } + y ^ { 2 } = 4$
b. Major axis $= 4$ in; minor axis $\approx 5.0$ in 
B)  a. $x ^ { 2 } + y ^ { 2 } = 16$
b. Major axis $\approx 2.5$ in; minor axis $= 2$ in 
C)  a. $x ^ { 2 } + y ^ { 2 } = 16$
b. Major axis $\approx 6.7$ in; minor axis $= 4$ in 
D)  a. $x ^ { 2 } + y ^ { 2 } = 4$
b. Major axis $\approx 5.0$ in; minor axis $= 4$ in

Question 5

An________ is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and two fixed points called________ is a constant.

Accepted Answer

The answer of An________ is a set of points (x,...

Question 6

The circle, the ellipse, the hyperbola, and the parabola are categories of ________sections.

Accepted Answer

The answer of The circle, the ellipse, the hyperbola, and...

Question 7

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The line segment perpendicular to the transverse axis passing through the center of a hyperbola, and with endpoints on the reference rectangle is called the ________axis.

Accepted Answer

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

Question 8

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given $( x - h ) ^ { 2 } = 4 p ( y - k )$ ), the ordered pairs representing the vertex and focus are________ and________, respectively. The directrix is the line defined by the equation________ .

Accepted Answer

(h, k); (h

Question 9

Graph the hyperbola. Identify the center and vertices.
-$\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 64 } = 1$

Accepted Answer

A)  center: $( 0,0 )$;
vertices: $( 0 , - 7 ) , ( 0,7 )$
  
B)  center: $( 7,8 )$;
vertices: $( 0 , - 7 ) , ( 0,7 )$
  
C)  center: $( 7,8 )$;
vertices: $( - 7,0 ) , ( 7,0 )$
  
D)  center: $( 0,0 )$;
vertices: $( - 7,0 ) , ( 7,0 )$
  
A)  center: $( 0,0 )$;
vertices: $( 0 , - 7 ) , ( 0,7 )$
  
B)  center: $( 7,8 )$;
vertices: $( 0 , - 7 ) , ( 0,7 )$
  
C)  center: $( 7,8 )$;
vertices: $( - 7,0 ) , ( 7,0 )$
  
D)  center: $( 0,0 )$;
vertices: $( - 7,0 ) , ( 7,0 )$

Question 10

Graph the ellipse.
-$$\frac { x ^ { 2 } } { 18 } + \frac { y ^ { 2 } } { 7 } = 1$$

Accepted Answer

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

Question 11

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The points where a hyperbola intersects the line through the foci are called the ________.

Accepted Answer

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

Question 12

Given an ellipse with major axis of length 2a and minor axis of length 2b, the area is given by A =ab.
The perimeter is approximated by $$P \approx \pi \sqrt { 2 \left( a ^ { 2 } + b ^ { 2 } \right) }$$ a. Determine the area of the ellipse. b. Approximate the perimeter.
-$$\frac { x ^ { 2 } } { 4 } + \frac { ( y - 6 ) ^ { 2 } } { 12 } = 1$$

Accepted Answer

A)  a. $A = 48 \pi$ square units
b. $P \approx 4 \pi \sqrt { 2 }$ units 
B)  a. $A = 48 \pi$ square units
b. $P \approx 12 \pi$ units 
C)  a. $A = 4 \pi \sqrt { 3 }$ square units
b. $P \approx 4 \pi \sqrt { 2 }$ units 
D)  a. $A = 4 \pi \sqrt { 3 }$ square units
b. $P \approx 12 \pi$ units 
A)  a. $A = 48 \pi$ square units
b. $P \approx 4 \pi \sqrt { 2 }$ units 
B)  a. $A = 48 \pi$ square units
b. $P \approx 12 \pi$ units 
C)  a. $A = 4 \pi \sqrt { 3 }$ square units
b. $P \approx 4 \pi \sqrt { 2 }$ units 
D)  a. $A = 4 \pi \sqrt { 3 }$ square units
b. $P \approx 12 \pi$ units

Question 13

Write the equation of the ellipse in standard form. Identify the vertices and foci.
-$$25 x ^ { 2 } + y ^ { 2 } + 14 y + 24 = 0$$

Accepted Answer

A)  $x ^ { 2 } + \frac { ( y + 7 ) ^ { 2 } } { 25 } = 1$
vertices: $( 0 , - 12 ) , ( 0 , - 2 )$
foci $( 0 , - 7 - 2 \sqrt { 6 } ) , ( 0 , - 7 + 2 \sqrt { 6 } )$ 
B)  $x ^ { 2 } + \frac { ( y + 7 ) ^ { 2 } } { 25 } = 1$
vertices: $( - 12,0 ) , ( - 2,0 )$
foci $( - 7 - 2 \sqrt { 6 } , 0 ) , ( - 7 + 2 \sqrt { 6 } , 0 )$ 
C)  $x ^ { 2 } + \frac { ( y - 7 ) ^ { 2 } } { 25 } = 1$
vertices: $( 2,0 ) , ( 12,0 )$
foci $( 7 - 2 \sqrt { 6 } , 0 ) , ( 7 + 2 \sqrt { 6 } , 0 )$ 
D)  $x ^ { 2 } + \frac { ( y - 7 ) ^ { 2 } } { 25 } = 1$
vertices: $( 0,2 ) , ( 0,12 )$
foci $( 0,7 - 2 \sqrt { 6 } ) , ( 0,7 + 2 \sqrt { 6 } )$ 
A)  $x ^ { 2 } + \frac { ( y + 7 ) ^ { 2 } } { 25 } = 1$
vertices: $( 0 , - 12 ) , ( 0 , - 2 )$
foci $( 0 , - 7 - 2 \sqrt { 6 } ) , ( 0 , - 7 + 2 \sqrt { 6 } )$ 
B)  $x ^ { 2 } + \frac { ( y + 7 ) ^ { 2 } } { 25 } = 1$
vertices: $( - 12,0 ) , ( - 2,0 )$
foci $( - 7 - 2 \sqrt { 6 } , 0 ) , ( - 7 + 2 \sqrt { 6 } , 0 )$ 
C)  $x ^ { 2 } + \frac { ( y - 7 ) ^ { 2 } } { 25 } = 1$
vertices: $( 2,0 ) , ( 12,0 )$
foci $( 7 - 2 \sqrt { 6 } , 0 ) , ( 7 + 2 \sqrt { 6 } , 0 )$ 
D)  $x ^ { 2 } + \frac { ( y - 7 ) ^ { 2 } } { 25 } = 1$
vertices: $( 0,2 ) , ( 0,12 )$
foci $( 0,7 - 2 \sqrt { 6 } ) , ( 0,7 + 2 \sqrt { 6 } )$

Question 14

The line through the foci intersects an ellipse at two points called________ .

Accepted Answer

The answer of The line through the foci intersects an...

Question 15

Solve the problem.
-A 20-in. satellite dish for a television has parabolic cross sections. A coordinate system is chosen so that the vertex of a cross section through the center of the dish is located at (0, 0). The equation of
The parabola is modeled by $x ^ { 2 } = 26.4 y$ where x and y are measured in inches. Where should the
Receiver be placed to maximize signal strength? That is, where is the focus?

Accepted Answer

A)  Focus: (0, 6.4); Place the receiver 6.4 in. above the center of the dish. 
B)  Focus: (0, 6.6); Place the receiver 6.6 in. above the center of the dish. 
C)  Focus: (0, 13.2); Place the receiver 13.2 in. above the center of the dish. 
D)  Focus: (0, 12.8); Place the receiver 12.8 in. above the center of the dish. 
A)  Focus: (0, 6.4); Place the receiver 6.4 in. above the center of the dish. 
B)  Focus: (0, 6.6); Place the receiver 6.6 in. above the center of the dish. 
C)  Focus: (0, 13.2); Place the receiver 13.2 in. above the center of the dish. 
D)  Focus: (0, 12.8); Place the receiver 12.8 in. above the center of the dish.

Question 16

Solve the problem.
-A planet's moon has an orbit that is elliptical with eccentricity 0.054 and with the planet at one focus. If the distance between the moon and the planet at perihelion (the closest point) is 364,100
Km, determine the distance at aphelion (the farthest point). Round to the nearest 100 km.

Accepted Answer

A)  384,900 km 
B)  769,800 km 
C)  749,000 km 
D)  405,700 km 
A)  384,900 km 
B)  769,800 km 
C)  749,000 km 
D)  405,700 km

Question 17

Find the standard form of the equation of the ellipse or hyperbola shown.
-

Accepted Answer

A)  $\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { ( y - 1 ) ^ { 2 } } { 5 } = 1$ 
B)  $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( x + 2 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x - 2 ) ^ { 2 } } { 16 } - \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$ 
A)  $\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { ( y - 1 ) ^ { 2 } } { 5 } = 1$ 
B)  $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( x + 2 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x - 2 ) ^ { 2 } } { 16 } - \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$

Question 18

Determine the eccentricity of the ellipse.
-$$\frac { ( x + 4 ) ^ { 2 } } { 144 } + \frac { ( y + 5 ) ^ { 2 } } { 169 } = 1$$

Accepted Answer

A)  $e = \frac { 12 } { 13 }$ 
B)  $e = \frac { 12 } { 5 }$ 
C)  $e = \frac { 4 } { 5 }$ 
D)  $e = \frac { 5 } { 13 }$ 
A)  $e = \frac { 12 } { 13 }$ 
B)  $e = \frac { 12 } { 5 }$ 
C)  $e = \frac { 4 } { 5 }$ 
D)  $e = \frac { 5 } { 13 }$

Question 19

Solve the problem.
-A homeowner wants to make an elliptical rug from a 30-foot by 10-foot rectangular piece of carpeting. 
a. What lengths of the major and minor axes would maximize the area of the new rug?
b. Write an equation of the ellipse with maximum area. Use a coordinate system with the origin at the center
Of the rug and horizontal major axis.

Accepted Answer

A)  a. Major axis: 32 feet. Minor axis: 16 feet
b. $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  a. Major axis: 15 feet. Minor axis: 5 feet
b. $\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 25 } = 1$ 
C)  a. Major axis: 30 feet. Minor axis: 10 feet
b. $\frac { x ^ { 2 } } { 900 } + \frac { y ^ { 2 } } { 100 } = 1$ 
D)  a. Major axis: 30 feet. Minor axis: 10 feet
b. $\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 25 } = 1$ 
A)  a. Major axis: 32 feet. Minor axis: 16 feet
b. $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  a. Major axis: 15 feet. Minor axis: 5 feet
b. $\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 25 } = 1$ 
C)  a. Major axis: 30 feet. Minor axis: 10 feet
b. $\frac { x ^ { 2 } } { 900 } + \frac { y ^ { 2 } } { 100 } = 1$ 
D)  a. Major axis: 30 feet. Minor axis: 10 feet
b. $\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 25 } = 1$

Question 20

Write the equation of the ellipse in standard form. Identify the vertices and foci.
-$$x ^ { 2 } + 81 y ^ { 2 } - 14 x - 32 = 0$$

Accepted Answer

A)  $\frac { ( x + 7 ) ^ { 2 } } { 81 } + y ^ { 2 } = 1$
vertices: $( - 16,0 ) , ( 2,0 )$
foci $( - 7 - 4 \sqrt { 5 } , 0 ) , ( - 7 + 4 \sqrt { 5 } , 0 )$ 
B)  $x ^ { 2 } + \frac { ( y + 7 ) ^ { 2 } } { 81 } = 1$
vertices: $( 0 , - 16 ) , ( 0,2 )$
foci $( 0 , - 7 - 4 \sqrt { 5 } ) , ( 0 , - 7 + 4 \sqrt { 5 } )$ 
C)  $\frac { ( x - 7 ) ^ { 2 } } { 81 } + y ^ { 2 } = 1$
vertices: $( - 2,0 ) , ( 16,0 )$
foci $( 7 - 4 \sqrt { 5 } , 0 ) , ( 7 + 4 \sqrt { 5 } , 0 )$ 
D)  $x ^ { 2 } + \frac { ( y - 7 ) ^ { 2 } } { 81 } = 1$
vertices: $( 0 , - 16 ) , ( 0,2 )$
foci $( 0,7 - 4 \sqrt { 5 } ) , ( 0,7 + 4 \sqrt { 5 } )$ 
A)  $\frac { ( x + 7 ) ^ { 2 } } { 81 } + y ^ { 2 } = 1$
vertices: $( - 16,0 ) , ( 2,0 )$
foci $( - 7 - 4 \sqrt { 5 } , 0 ) , ( - 7 + 4 \sqrt { 5 } , 0 )$ 
B)  $x ^ { 2 } + \frac { ( y + 7 ) ^ { 2 } } { 81 } = 1$
vertices: $( 0 , - 16 ) , ( 0,2 )$
foci $( 0 , - 7 - 4 \sqrt { 5 } ) , ( 0 , - 7 + 4 \sqrt { 5 } )$ 
C)  $\frac { ( x - 7 ) ^ { 2 } } { 81 } + y ^ { 2 } = 1$
vertices: $( - 2,0 ) , ( 16,0 )$
foci $( 7 - 4 \sqrt { 5 } , 0 ) , ( 7 + 4 \sqrt { 5 } , 0 )$ 
D)  $x ^ { 2 } + \frac { ( y - 7 ) ^ { 2 } } { 81 } = 1$
vertices: $( 0 , - 16 ) , ( 0,2 )$
foci $( 0,7 - 4 \sqrt { 5 } ) , ( 0,7 + 4 \sqrt { 5 } )$

An equation of a parabola $( x - h ) ^ { 2 } = 4 p ( y - k )$ is given. Graph the parabola. Identify the vertex and the focal diameter. - $( x + 3 ) ^ { 2 } = - 4 ( y + 4 )$

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the vertex and the focal diameter. - $y ^ { 2 } - 8 y - 12 x - 8 = 0$

An is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and two fixed points called is a constant.

The circle, the ellipse, the hyperbola, and the parabola are categories of ________sections.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The line segment perpendicular to the transverse axis passing through the center of a hyperbola, and with endpoints on the reference rectangle is called the ________axis.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given $( x - h ) ^ { 2 } = 4 p ( y - k )$ ), the ordered pairs representing the vertex and focus are and, respectively. The directrix is the line defined by the equation .

Graph the hyperbola. Identify the center and vertices. - $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 64 } = 1$

Graph the ellipse. - $\frac { x ^ { 2 } } { 18 } + \frac { y ^ { 2 } } { 7 } = 1$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The points where a hyperbola intersects the line through the foci are called the ________.

Write the equation of the ellipse in standard form. Identify the vertices and foci. - $25 x ^ { 2 } + y ^ { 2 } + 14 y + 24 = 0$

The line through the foci intersects an ellipse at two points called________ .

Find the standard form of the equation of the ellipse or hyperbola shown. -

Determine the eccentricity of the ellipse. - $\frac { ( x + 4 ) ^ { 2 } } { 144 } + \frac { ( y + 5 ) ^ { 2 } } { 169 } = 1$

Write the equation of the ellipse in standard form. Identify the vertices and foci. - $x ^ { 2 } + 81 y ^ { 2 } - 14 x - 32 = 0$

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

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Exam 7: Analytic Geometry

An equation of a parabola (x−h)2=4p(y−k)( x - h ) ^ { 2 } = 4 p ( y - k )(x−h)2=4p(y−k) is given. Graph the parabola. Identify the vertex and the focal diameter. - (x+3)2=−4(y+4)( x + 3 ) ^ { 2 } = - 4 ( y + 4 )(x+3)2=−4(y+4)

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the vertex and the focal diameter. - y2−8y−12x−8=0y ^ { 2 } - 8 y - 12 x - 8 = 0y2−8y−12x−8=0

An________ is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and two fixed points called________ is a constant.

The circle, the ellipse, the hyperbola, and the parabola are categories of ________sections.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The line segment perpendicular to the transverse axis passing through the center of a hyperbola, and with endpoints on the reference rectangle is called the ________axis.

Graph the hyperbola. Identify the center and vertices. - x249−y264=1\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 64 } = 149x2​−64y2​=1

Graph the ellipse. - x218+y27=1\frac { x ^ { 2 } } { 18 } + \frac { y ^ { 2 } } { 7 } = 118x2​+7y2​=1

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The points where a hyperbola intersects the line through the foci are called the ________.

Write the equation of the ellipse in standard form. Identify the vertices and foci. - 25x2+y2+14y+24=025 x ^ { 2 } + y ^ { 2 } + 14 y + 24 = 025x2+y2+14y+24=0

The line through the foci intersects an ellipse at two points called________ .

Find the standard form of the equation of the ellipse or hyperbola shown. -

Determine the eccentricity of the ellipse. - (x+4)2144+(y+5)2169=1\frac { ( x + 4 ) ^ { 2 } } { 144 } + \frac { ( y + 5 ) ^ { 2 } } { 169 } = 1144(x+4)2​+169(y+5)2​=1

Write the equation of the ellipse in standard form. Identify the vertices and foci. - x2+81y2−14x−32=0x ^ { 2 } + 81 y ^ { 2 } - 14 x - 32 = 0x2+81y2−14x−32=0

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

An equation of a parabola $( x - h ) ^ { 2 } = 4 p ( y - k )$ is given. Graph the parabola. Identify the vertex and the focal diameter. - $( x + 3 ) ^ { 2 } = - 4 ( y + 4 )$

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the vertex and the focal diameter. - $y ^ { 2 } - 8 y - 12 x - 8 = 0$

An is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and two fixed points called is a constant.

Graph the hyperbola. Identify the center and vertices. - $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 64 } = 1$

Graph the ellipse. - $\frac { x ^ { 2 } } { 18 } + \frac { y ^ { 2 } } { 7 } = 1$

Write the equation of the ellipse in standard form. Identify the vertices and foci. - $25 x ^ { 2 } + y ^ { 2 } + 14 y + 24 = 0$

Determine the eccentricity of the ellipse. - $\frac { ( x + 4 ) ^ { 2 } } { 144 } + \frac { ( y + 5 ) ^ { 2 } } { 169 } = 1$

Write the equation of the ellipse in standard form. Identify the vertices and foci. - $x ^ { 2 } + 81 y ^ { 2 } - 14 x - 32 = 0$