Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Graph the ellipse.
-$$\frac { 25 ( x - 5 ) ^ { 2 } } { 81 } + \frac { 25 ( y + 1 ) ^ { 2 } } { 196 } = 1$$

Accepted Answer

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

Question 4

Fill in the blanks. Le $| \boldsymbol { p } |$ | represent the focal length (the distance between the vertex and the focus).
-If the directrix of a parabola is given by y = -1 and the focus is (-3, 5), then the vertex is given by the ordered pair ________ and the value of p is ________.

Accepted Answer

A)  (-3, 2); 3 
B)  (3, 2), -3 
C)  (-3, 6); -2 
D)  (-2, 2); -1 
A)  (-3, 2); 3 
B)  (3, 2), -3 
C)  (-3, 6); -2 
D)  (-2, 2); -1

Question 5

Solve the system of equations.
-$$\begin{array} { l } 
\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1 \
y = - x ^ { 2 } + 4
\end{array}$$

Accepted Answer

A)  $\{ ( 0,4 ) , ( - 2,0 ) , ( 2,0 ) \}$ 
B)  $\{ ( 0 , - 4 ) , ( - 2,0 ) , ( 2,0 ) \}$ 
C)  $\{ ( 0,4 ) , ( 2,0 ) \}$ 
D)  $\{ ( 0 , - 4 ) , ( 0,4 ) , ( - 2,0 ) , ( 2,0 ) \}$ 
A)  $\{ ( 0,4 ) , ( - 2,0 ) , ( 2,0 ) \}$ 
B)  $\{ ( 0 , - 4 ) , ( - 2,0 ) , ( 2,0 ) \}$ 
C)  $\{ ( 0,4 ) , ( 2,0 ) \}$ 
D)  $\{ ( 0 , - 4 ) , ( 0,4 ) , ( - 2,0 ) , ( 2,0 ) \}$

Question 6

Solve the problem.
-A window above a door is to be made in the shape of a semiellipse. If the window is 12 feet at the base and 4 feet high at the center, determine the distance from the center at which the foci are
Located. Round to one decimal place.

Accepted Answer

A)  11.3 feet 
B)  20.0 feet 
C)  4.5 feet 
D)  8.9 feet 
A)  11.3 feet 
B)  20.0 feet 
C)  4.5 feet 
D)  8.9 feet

Question 7

A model of the form $y ^ { 2 } = 4 p x$ is given. Identify the focus, and write an equation for the directrix.
-$$y ^ { 2 } = - 3 x$$

Accepted Answer

A)  focus: $\left( - \frac { 3 } { 4 } , 0 \right)$; directrix: $x = \frac { 3 } { 4 }$ 
B)  focus: $\left( 0 , \frac { 3 } { 4 } \right)$; directrix: $y = - \frac { 3 } { 4 }$ 
C)  focus: $\left( - \frac { 3 } { 4 } , 0 \right) ;$ directrix: $x = - \frac { 3 } { 4 }$ 
D)  focus: $\left( 0 , - \frac { 3 } { 4 } \right) ;$ directrix: $y = \frac { 3 } { 4 }$ 
A)  focus: $\left( - \frac { 3 } { 4 } , 0 \right)$; directrix: $x = \frac { 3 } { 4 }$ 
B)  focus: $\left( 0 , \frac { 3 } { 4 } \right)$; directrix: $y = - \frac { 3 } { 4 }$ 
C)  focus: $\left( - \frac { 3 } { 4 } , 0 \right) ;$ directrix: $x = - \frac { 3 } { 4 }$ 
D)  focus: $\left( 0 , - \frac { 3 } { 4 } \right) ;$ directrix: $y = \frac { 3 } { 4 }$

Question 8

Graph the parabola. Identify the focus.
-$2 y^{2}=-4 x$

Accepted Answer

A)  
focus: $\left( 0 , - \frac { 1 } { 2 } \right)$ 
B)  
$\text { focus: }\left(-\frac{1}{2}, 0\right)$
focus: $\left( - \frac { 1 } { 2 } , 0 \right)$ 
C)  
focus: $\left( \frac { 1 } { 2 } , 0 \right)$ 
D)  
focus: $\left( 0 , \frac { 1 } { 2 } \right)$ 
A)  
focus: $\left( 0 , - \frac { 1 } { 2 } \right)$ 
B)  
$\text { focus: }\left(-\frac{1}{2}, 0\right)$
focus: $\left( - \frac { 1 } { 2 } , 0 \right)$ 
C)  
focus: $\left( \frac { 1 } { 2 } , 0 \right)$ 
D)  
focus: $\left( 0 , \frac { 1 } { 2 } \right)$

Question 9

Solve the problem.
-Suppose that two microphones 2,800 m apart at points A = (1,400, 0) and B = (-1,400, 0) detect the sound of a rifle shot. The time difference between the sound detected at A and the sound detected at B is 2 sec. If sound travels at approximately 330 m/sec, find an equation of the hyperbola with foci
At A and B defining the points where the shooter may be located.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 330 ^ { 2 } } - \frac { y ^ { 2 } } { 1,361 ^ { 2 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 1,400 ^ { 2 } } - \frac { y ^ { 2 } } { 330 ^ { 2 } } = 1$ 
C)  $\frac { x ^ { 2 } } { 2,800 ^ { 2 } } - \frac { y ^ { 2 } } { 2,721 ^ { 2 } } = 1$ 
D)  $\frac { y ^ { 2 } } { 1,361 ^ { 2 } } - \frac { x ^ { 2 } } { 330 ^ { 2 } } = 1$ 
A)  $\frac { x ^ { 2 } } { 330 ^ { 2 } } - \frac { y ^ { 2 } } { 1,361 ^ { 2 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 1,400 ^ { 2 } } - \frac { y ^ { 2 } } { 330 ^ { 2 } } = 1$ 
C)  $\frac { x ^ { 2 } } { 2,800 ^ { 2 } } - \frac { y ^ { 2 } } { 2,721 ^ { 2 } } = 1$ 
D)  $\frac { y ^ { 2 } } { 1,361 ^ { 2 } } - \frac { x ^ { 2 } } { 330 ^ { 2 } } = 1$

Question 10

The center of an ellipse is the midpoint of the________ axis.

Accepted Answer

The answer of The center of an ellipse is the...

Question 11

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given $\frac { ( x - h ) ^ { 2 } } { a ^ { 2 } } - \frac { ( y - k ) ^ { 2 } } { b ^ { 2 } } = 1$ e ordered pairs representing the vertices are ________and________ .

Accepted Answer

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

Question 12

Graph the ellipse. Identify the foci and vertices.
-$$25 x ^ { 2 } + 9 y ^ { 2 } = 225$$

Accepted Answer

A)  foci: $( 0 , - 4 ) , ( 0,4 )$;
vertices: $( - 5,0 ) , ( 5,0 )$
  
B)  foci: $( - 4,0 ) , ( 4,0 )$;
vertices: $( - 5,0 ) , ( 5,0 )$
  
C)  foci: $( - 4,0 ) , ( 4,0 )$;
vertices: $( 0 , - 5 ) , ( 0,5 )$
  
D)  foci: $( 0 , - 4 ) , ( 0,4 )$;
vertices: $( 0 , - 5 ) , ( 0,5 )$
  
A)  foci: $( 0 , - 4 ) , ( 0,4 )$;
vertices: $( - 5,0 ) , ( 5,0 )$
  
B)  foci: $( - 4,0 ) , ( 4,0 )$;
vertices: $( - 5,0 ) , ( 5,0 )$
  
C)  foci: $( - 4,0 ) , ( 4,0 )$;
vertices: $( 0 , - 5 ) , ( 0,5 )$
  
D)  foci: $( 0 , - 4 ) , ( 0,4 )$;
vertices: $( 0 , - 5 ) , ( 0,5 )$

Question 13

Write the standard form of an equation of the ellipse subject to the given conditions.
-Endpoints of minor axis: $( \sqrt { 31 } , 0 )$ and $( - \sqrt { 31 } , 0 )$
Foci: $( 0,10 )$ and $( 0 , - 10 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 41 } + \frac { y ^ { 2 } } { 31 } = 1$ 
B)  $\frac { x ^ { 2 } } { 31 } + \frac { y ^ { 2 } } { 41 } = 1$ 
C)  $\frac { x ^ { 2 } } { 31 } + \frac { y ^ { 2 } } { 131 } = 1$ 
D)  $\frac { x ^ { 2 } } { 131 } + \frac { y ^ { 2 } } { 31 } = 1$ 
A)  $\frac { x ^ { 2 } } { 41 } + \frac { y ^ { 2 } } { 31 } = 1$ 
B)  $\frac { x ^ { 2 } } { 31 } + \frac { y ^ { 2 } } { 41 } = 1$ 
C)  $\frac { x ^ { 2 } } { 31 } + \frac { y ^ { 2 } } { 131 } = 1$ 
D)  $\frac { x ^ { 2 } } { 131 } + \frac { y ^ { 2 } } { 31 } = 1$

Question 14

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given $\frac { ( y - k ) ^ { 2 } } { a ^ { 2 } } - \frac { ( x - h ) ^ { 2 } } { b ^ { 2 } } = 1$ e ordered pairs representing the vertices are ________and________ .

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Choose the one alternative that best completes the statement or answers the question.
A model of the form $x ^ { 2 } = 4 p y$ is given. Identify the focus, and write an equation for the directrix.
-$$x ^ { 2 } = 32 y$$

Accepted Answer

A)  focus: $( 0,8 )$; directrix: $y = - 8$ 
B)  focus: $( 8,0 )$; directrix: $y = - 8$ 
C)  focus: $( - 8,0 )$; directrix: $y = 8$ 
D)  focus: $( 0 , - 8 )$; directrix: $y = 8$ 
A)  focus: $( 0,8 )$; directrix: $y = - 8$ 
B)  focus: $( 8,0 )$; directrix: $y = - 8$ 
C)  focus: $( - 8,0 )$; directrix: $y = 8$ 
D)  focus: $( 0 , - 8 )$; directrix: $y = 8$

Question 17

Identify the vertices and the foci.
-$$( x - 6 ) ^ { 2 } + \frac { y ^ { 2 } } { 25 } = 1$$

Accepted Answer

A)  vertices: $( 0,5 )$ and $( 0 , - 5 )$;
foci: $( 0,2 \sqrt { 6 } )$ and $( 0 , - 2 \sqrt { 6 } )$ 
B)  vertices: $( 6,5 )$ and $( 6 , - 5 )$;
foci: $( 6,2 )$ and $( 6 , - 2 )$ 
C)  vertices: $( 0,5 )$ and $( 0 , - 5 )$;
foci: $( 0,2 )$ and $( 0 , - 2 )$ 
D)  vertices: $( 6,5 )$ and $( 6 , - 5 )$;
foci: $( 6,2 \sqrt { 6 } )$ and $( 6 , - 2 \sqrt { 6 } )$ 
A)  vertices: $( 0,5 )$ and $( 0 , - 5 )$;
foci: $( 0,2 \sqrt { 6 } )$ and $( 0 , - 2 \sqrt { 6 } )$ 
B)  vertices: $( 6,5 )$ and $( 6 , - 5 )$;
foci: $( 6,2 )$ and $( 6 , - 2 )$ 
C)  vertices: $( 0,5 )$ and $( 0 , - 5 )$;
foci: $( 0,2 )$ and $( 0 , - 2 )$ 
D)  vertices: $( 6,5 )$ and $( 6 , - 5 )$;
foci: $( 6,2 \sqrt { 6 } )$ and $( 6 , - 2 \sqrt { 6 } )$

Question 18

Identify the center of the ellipse and the foci.
-$\frac { 25 ( x - 3 ) ^ { 2 } } { 169 } + \frac { 49 ( y + 6 ) ^ { 2 } } { 225 } = 1$

Accepted Answer

A)  center: $( - 3,6 )$;
foci: $\left( - 3 + \frac { 4 \sqrt { 166 } } { 35 } , 6 \right)$ and $\left( - 3 - \frac { 4 \sqrt { 166 } } { 35 } , 6 \right)$ 
B)  center: $( - 6,3 )$;
foci: $( - 6 + 4 \sqrt { 166 } , 3 )$ and $( - 6 - 4 \sqrt { 166 } , 3 )$ 
C)  center: $( 6 , - 3 )$;
foci: $( 6 + 4 \sqrt { 166 } , - 3 )$ and $( 6 - 4 \sqrt { 166 } , - 3 )$ 
D)  center: $( 3 , - 6 )$;
foci: $\left( 3 + \frac { 4 \sqrt { 166 } } { 35 } , - 6 \right)$ and $\left( 3 - \frac { 4 \sqrt { 166 } } { 35 } , - 6 \right)$ 
A)  center: $( - 3,6 )$;
foci: $\left( - 3 + \frac { 4 \sqrt { 166 } } { 35 } , 6 \right)$ and $\left( - 3 - \frac { 4 \sqrt { 166 } } { 35 } , 6 \right)$ 
B)  center: $( - 6,3 )$;
foci: $( - 6 + 4 \sqrt { 166 } , 3 )$ and $( - 6 - 4 \sqrt { 166 } , 3 )$ 
C)  center: $( 6 , - 3 )$;
foci: $( 6 + 4 \sqrt { 166 } , - 3 )$ and $( 6 - 4 \sqrt { 166 } , - 3 )$ 
D)  center: $( 3 , - 6 )$;
foci: $\left( 3 + \frac { 4 \sqrt { 166 } } { 35 } , - 6 \right)$ and $\left( 3 - \frac { 4 \sqrt { 166 } } { 35 } , - 6 \right)$

Question 19

Identify the vertices and the foci.
-$$\frac { x ^ { 2 } } { 14 } + \frac { y ^ { 2 } } { 2 } = 1$$

Accepted Answer

A)  vertices: $( 0,14 )$ and $( 0 , - 14 )$;
foci: $( 0,12 )$ and $( 0 , - 12 )$ 
B)  vertices: $( 14,0 )$ and $( - 14,0 )$;
foci: $( 12,0 )$ and $( - 12,0 )$ 
C)  vertices: $( 0 , \sqrt { 14 } )$ and $( 0 , - \sqrt { 14 } )$
foci: $( 0,2 \sqrt { 3 } )$ and $( 0 , - 2 \sqrt { 3 } )$ 
D)  vertices: $( \sqrt { 14 } , 0 )$ and $( - \sqrt { 14 } , 0 )$;
foci: $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$ 
A)  vertices: $( 0,14 )$ and $( 0 , - 14 )$;
foci: $( 0,12 )$ and $( 0 , - 12 )$ 
B)  vertices: $( 14,0 )$ and $( - 14,0 )$;
foci: $( 12,0 )$ and $( - 12,0 )$ 
C)  vertices: $( 0 , \sqrt { 14 } )$ and $( 0 , - \sqrt { 14 } )$
foci: $( 0,2 \sqrt { 3 } )$ and $( 0 , - 2 \sqrt { 3 } )$ 
D)  vertices: $( \sqrt { 14 } , 0 )$ and $( - \sqrt { 14 } , 0 )$;
foci: $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$

Question 20

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given $y ^ { 2 } = 4 p x$ with p < 0, the parabola opens (upward/downward/ left/right).

Accepted Answer

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

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

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

Graph the ellipse. - $\frac { 25 ( x - 5 ) ^ { 2 } } { 81 } + \frac { 25 ( y + 1 ) ^ { 2 } } { 196 } = 1$

Fill in the blanks. Le $| \boldsymbol { p } |$ | represent the focal length (the distance between the vertex and the focus). -If the directrix of a parabola is given by y = -1 and the focus is (-3, 5), then the vertex is given by the ordered pair and the value of p is .

Solve the system of equations. - +=1 y=-+4

Solve the problem. -A window above a door is to be made in the shape of a semiellipse. If the window is 12 feet at the base and 4 feet high at the center, determine the distance from the center at which the foci are Located. Round to one decimal place.

A model of the form $y ^ { 2 } = 4 p x$ is given. Identify the focus, and write an equation for the directrix. - $y ^ { 2 } = - 3 x$

Graph the parabola. Identify the focus. - $2 y^{2}=-4 x$

The center of an ellipse is the midpoint of the________ axis.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given $\frac { ( x - h ) ^ { 2 } } { a ^ { 2 } } - \frac { ( y - k ) ^ { 2 } } { b ^ { 2 } } = 1$ e ordered pairs representing the vertices are and .

Graph the ellipse. Identify the foci and vertices. - $25 x ^ { 2 } + 9 y ^ { 2 } = 225$

Write the standard form of an equation of the ellipse subject to the given conditions. -Endpoints of minor axis: $( \sqrt { 31 } , 0 )$ and $( - \sqrt { 31 } , 0 )$ Foci: $( 0,10 )$ and $( 0 , - 10 )$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given $\frac { ( y - k ) ^ { 2 } } { a ^ { 2 } } - \frac { ( x - h ) ^ { 2 } } { b ^ { 2 } } = 1$ e ordered pairs representing the vertices are and .

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

Choose the one alternative that best completes the statement or answers the question. A model of the form $x ^ { 2 } = 4 p y$ is given. Identify the focus, and write an equation for the directrix. - $x ^ { 2 } = 32 y$

Identify the vertices and the foci. - $( x - 6 ) ^ { 2 } + \frac { y ^ { 2 } } { 25 } = 1$

Identify the center of the ellipse and the foci. - $\frac { 25 ( x - 3 ) ^ { 2 } } { 169 } + \frac { 49 ( y + 6 ) ^ { 2 } } { 225 } = 1$

Identify the vertices and the foci. - $\frac { x ^ { 2 } } { 14 } + \frac { y ^ { 2 } } { 2 } = 1$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given $y ^ { 2 } = 4 p x$ with p < 0, the parabola opens (upward/downward/ left/right).

Equations and Inequalities

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Exam 7: Analytic Geometry

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

Graph the ellipse. - 25(x−5)281+25(y+1)2196=1\frac { 25 ( x - 5 ) ^ { 2 } } { 81 } + \frac { 25 ( y + 1 ) ^ { 2 } } { 196 } = 18125(x−5)2​+19625(y+1)2​=1

Fill in the blanks. Le ∣p∣| \boldsymbol { p } |∣p∣ | represent the focal length (the distance between the vertex and the focus). -If the directrix of a parabola is given by y = -1 and the focus is (-3, 5), then the vertex is given by the ordered pair ________ and the value of p is ________.

Solve the system of equations. - +=1 y=-+4

Solve the problem. -A window above a door is to be made in the shape of a semiellipse. If the window is 12 feet at the base and 4 feet high at the center, determine the distance from the center at which the foci are Located. Round to one decimal place.

A model of the form y2=4pxy ^ { 2 } = 4 p xy2=4px is given. Identify the focus, and write an equation for the directrix. - y2=−3xy ^ { 2 } = - 3 xy2=−3x

Graph the parabola. Identify the focus. - 2y2=−4x2 y^{2}=-4 x2y2=−4x

The center of an ellipse is the midpoint of the________ axis.

Graph the ellipse. Identify the foci and vertices. - 25x2+9y2=22525 x ^ { 2 } + 9 y ^ { 2 } = 22525x2+9y2=225

Write the standard form of an equation of the ellipse subject to the given conditions. -Endpoints of minor axis: (31,0)( \sqrt { 31 } , 0 )(31​,0) and (−31,0)( - \sqrt { 31 } , 0 )(−31​,0) Foci: (0,10)( 0,10 )(0,10) and (0,−10)( 0 , - 10 )(0,−10)

Choose the one alternative that best completes the statement or answers the question. A model of the form x2=4pyx ^ { 2 } = 4 p yx2=4py is given. Identify the focus, and write an equation for the directrix. - x2=32yx ^ { 2 } = 32 yx2=32y

Identify the vertices and the foci. - (x−6)2+y225=1( x - 6 ) ^ { 2 } + \frac { y ^ { 2 } } { 25 } = 1(x−6)2+25y2​=1

Identify the center of the ellipse and the foci. - 25(x−3)2169+49(y+6)2225=1\frac { 25 ( x - 3 ) ^ { 2 } } { 169 } + \frac { 49 ( y + 6 ) ^ { 2 } } { 225 } = 116925(x−3)2​+22549(y+6)2​=1

Identify the vertices and the foci. - x214+y22=1\frac { x ^ { 2 } } { 14 } + \frac { y ^ { 2 } } { 2 } = 114x2​+2y2​=1

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given y2=4pxy ^ { 2 } = 4 p xy2=4px with p < 0, the parabola opens (upward/downward/ left/right).

Equations and Inequalities

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Polynomial and Rational Functions

Exponential and Logarithmic Functions

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Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Graph the ellipse. - $\frac { 25 ( x - 5 ) ^ { 2 } } { 81 } + \frac { 25 ( y + 1 ) ^ { 2 } } { 196 } = 1$

Fill in the blanks. Le $| \boldsymbol { p } |$ | represent the focal length (the distance between the vertex and the focus). -If the directrix of a parabola is given by y = -1 and the focus is (-3, 5), then the vertex is given by the ordered pair and the value of p is .

A model of the form $y ^ { 2 } = 4 p x$ is given. Identify the focus, and write an equation for the directrix. - $y ^ { 2 } = - 3 x$

Graph the parabola. Identify the focus. - $2 y^{2}=-4 x$

Graph the ellipse. Identify the foci and vertices. - $25 x ^ { 2 } + 9 y ^ { 2 } = 225$

Write the standard form of an equation of the ellipse subject to the given conditions. -Endpoints of minor axis: $( \sqrt { 31 } , 0 )$ and $( - \sqrt { 31 } , 0 )$ Foci: $( 0,10 )$ and $( 0 , - 10 )$

Choose the one alternative that best completes the statement or answers the question. A model of the form $x ^ { 2 } = 4 p y$ is given. Identify the focus, and write an equation for the directrix. - $x ^ { 2 } = 32 y$

Identify the vertices and the foci. - $( x - 6 ) ^ { 2 } + \frac { y ^ { 2 } } { 25 } = 1$

Identify the center of the ellipse and the foci. - $\frac { 25 ( x - 3 ) ^ { 2 } } { 169 } + \frac { 49 ( y + 6 ) ^ { 2 } } { 225 } = 1$

Identify the vertices and the foci. - $\frac { x ^ { 2 } } { 14 } + \frac { y ^ { 2 } } { 2 } = 1$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given $y ^ { 2 } = 4 p x$ with p < 0, the parabola opens (upward/downward/ left/right).