Question 1

When referring to the standard form of an equation of an ellipse, the________ , e, is defined as $e = \frac { \square } { \square }$

Accepted Answer

The answer of When referring to the standard form of...

Question 2

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the
focus and the equation of the directrix.
-$$4 x ^ { 2 } + 28 x + 40 y + 209 = 0$$

Accepted Answer

A)  $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = - 10 ( y + 4 )$
focus: $\left( - \frac { 7 } { 2 } , - \frac { 13 } { 2 } \right) ;$ directrix $: y = - \frac { 3 } { 2 }$ 
B)  $( x + 14 ) ^ { 2 } = - 40 \left( y + \frac { 13 } { 40 } \right)$
focus: $\left( - 14 , - \frac { 387 } { 40 } \right) ;$ directrix: $y = - \frac { 413 } { 40 }$ 
C)  $\left( x - \frac { 7 } { 2 } \right) ^ { 2 } = - 10 ( y + 4 )$
focus: $\left( \frac { 7 } { 2 } , - \frac { 13 } { 2 } \right) ;$ directrix: $y = - \frac { 3 } { 2 }$ 
D)  $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = - 10 ( y - 4 )$
focus: $\left( - \frac { 7 } { 2 } , \frac { 3 } { 2 } \right)$; directrix: $y = \frac { 13 } { 2 }$ 
A)  $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = - 10 ( y + 4 )$
focus: $\left( - \frac { 7 } { 2 } , - \frac { 13 } { 2 } \right) ;$ directrix $: y = - \frac { 3 } { 2 }$ 
B)  $( x + 14 ) ^ { 2 } = - 40 \left( y + \frac { 13 } { 40 } \right)$
focus: $\left( - 14 , - \frac { 387 } { 40 } \right) ;$ directrix: $y = - \frac { 413 } { 40 }$ 
C)  $\left( x - \frac { 7 } { 2 } \right) ^ { 2 } = - 10 ( y + 4 )$
focus: $\left( \frac { 7 } { 2 } , - \frac { 13 } { 2 } \right) ;$ directrix: $y = - \frac { 3 } { 2 }$ 
D)  $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = - 10 ( y - 4 )$
focus: $\left( - \frac { 7 } { 2 } , \frac { 3 } { 2 } \right)$; directrix: $y = \frac { 13 } { 2 }$

Question 3

Write the standard form of an equation of the ellipse subject to the given conditions.
-Center $( 0,0 )$; Eccentricity: $\frac { 24 } { 25 }$; Major axis vertical of length 50 units

Accepted Answer

A)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 625 } = 1$ 
B)  $\frac { x ^ { 2 } } { 576 } + \frac { y ^ { 2 } } { 625 } = 1$ 
C)  $\frac { x ^ { 2 } } { 625 } + \frac { y ^ { 2 } } { 49 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 576 } = 1$ 
A)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 625 } = 1$ 
B)  $\frac { x ^ { 2 } } { 576 } + \frac { y ^ { 2 } } { 625 } = 1$ 
C)  $\frac { x ^ { 2 } } { 625 } + \frac { y ^ { 2 } } { 49 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 576 } = 1$

Question 4

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the
vertex and the equation of the directrix.
-$$y ^ { 2 } + 16 x - 4 y + 52 = 0$$

Accepted Answer

A)  $( y + 2 ) ^ { 2 } = - 16 ( x - 3 )$
vertex: $( - 3,2 )$; focus: $( 7,2 )$ 
B)  $( y + 2 ) ^ { 2 } = - 16 ( x - 3 )$
vertex: $( 3 , - 2 )$; focus: $( 7 , - 2 )$ 
C)  $( y - 2 ) ^ { 2 } = - 16 ( x + 3 )$
vertex: $( - 3,2 )$; focus: $( - 7,2 )$ 
D)  $( y - 2 ) ^ { 2 } = - 16 ( x + 3 )$
vertex: $( 3 , - 2 )$; focus: $( - 7 , - 2 )$ 
A)  $( y + 2 ) ^ { 2 } = - 16 ( x - 3 )$
vertex: $( - 3,2 )$; focus: $( 7,2 )$ 
B)  $( y + 2 ) ^ { 2 } = - 16 ( x - 3 )$
vertex: $( 3 , - 2 )$; focus: $( 7 , - 2 )$ 
C)  $( y - 2 ) ^ { 2 } = - 16 ( x + 3 )$
vertex: $( - 3,2 )$; focus: $( - 7,2 )$ 
D)  $( y - 2 ) ^ { 2 } = - 16 ( x + 3 )$
vertex: $( 3 , - 2 )$; focus: $( - 7 , - 2 )$

Question 5

Graph the ellipse. Identify the foci and vertices.
-$$25 ( x + 2 ) ^ { 2 } + 9 ( x + 4 ) ^ { 2 } = 225$$

Accepted Answer

A)  foci: $( - 2,0 ) , ( - 2 , - 8 )$;
vertices: $( - 2 , - 9 ) , ( - 2,1 )$
  
B)  foci: $( 6,4 ) , ( - 2,4 )$;
vertices: $( 7,4 ) , ( - 3,4 )$
  
C)  foci: $( 2,8 ) , ( 2,0 )$;
vertices: $( 2,9 ) , ( 2 , - 1 )$
  
D)  foci: $( 2 , - 4 ) , ( - 6 , - 4 )$;
vertices: $( 3 , - 4 ) , ( - 7 , - 4 )$
  
A)  foci: $( - 2,0 ) , ( - 2 , - 8 )$;
vertices: $( - 2 , - 9 ) , ( - 2,1 )$
  
B)  foci: $( 6,4 ) , ( - 2,4 )$;
vertices: $( 7,4 ) , ( - 3,4 )$
  
C)  foci: $( 2,8 ) , ( 2,0 )$;
vertices: $( 2,9 ) , ( 2 , - 1 )$
  
D)  foci: $( 2 , - 4 ) , ( - 6 , - 4 )$;
vertices: $( 3 , - 4 ) , ( - 7 , - 4 )$

Question 6

Determine the standard form of an equation of the parabola subject to the given conditions.
-Vertex: $( - 1 , - 3 )$; Directrix: $x = - 5$

Accepted Answer

A)  $( y + 3 ) ^ { 2 } = 16 ( x + 1 )$ 
B)  $( x + 1 ) ^ { 2 } = 16 ( y + 3 )$ 
C)  $( y + 3 ) ^ { 2 } = - 5 ( x + 1 )$ 
D)  $( x + 1 ) ^ { 2 } = - 5 ( y + 3 )$ 
A)  $( y + 3 ) ^ { 2 } = 16 ( x + 1 )$ 
B)  $( x + 1 ) ^ { 2 } = 16 ( y + 3 )$ 
C)  $( y + 3 ) ^ { 2 } = - 5 ( x + 1 )$ 
D)  $( x + 1 ) ^ { 2 } = - 5 ( y + 3 )$

Question 7

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-When referring to the standard form of an equation of a hyperbola, the________ , e, is defined as e $= \frac { \square } { \square }$

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.
-The midpoint of the transverse axis is the ________of the hyperbola.

Accepted Answer

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

Question 9

An equation of a parabola $( y - k ) ^ { 2 } = 4 p ( x - h )$ is given. Graph the parabola. Write the equation for the directrix and axis of symmetry.
-$$( y - 1 ) ^ { 2 } = 12 ( x - 2 )$$

Accepted Answer

A)  directrix: $x = - 1$;
axis of symmetry: $y = 1$
  
B)  directrix: $y = - 4$;
 axis of symmetry: $x = - 2$
  
C)  directrix: $y = - 2$;
axis of symmetry: $x = 2$ 
  
D)  directrix: $x = - 5$;
axis of symmetry: $y = - 1$
  
A)  directrix: $x = - 1$;
axis of symmetry: $y = 1$
  
B)  directrix: $y = - 4$;
 axis of symmetry: $x = - 2$
  
C)  directrix: $y = - 2$;
axis of symmetry: $x = 2$ 
  
D)  directrix: $x = - 5$;
axis of symmetry: $y = - 1$

Question 10

An equation of the form $x ^ { 2 } = 4 p y$ is given. Identify the focus and the endpoints of the latus rectum.
-$$x ^ { 2 } = - 12 y$$

Accepted Answer

A)  focus: $( 0 , - 3 )$; endpoints of latus rectum: $( - 12 , - 3 ) ; ( 12 , - 3 )$ 
B)  focus: $( 0,3 )$; endpoints of latus rectum: $( - 12,3 ) ; ( 12,3 )$ 
C)  focus: $( 0 , - 3 )$; endpoints of latus rectum: $( - 6 , - 3 ) ; ( 6 , - 3 )$ 
D)  focus: $( 0,3 )$; endpoints of latus rectum: $( - 6,3 ) ; ( 6,3 )$ 
A)  focus: $( 0 , - 3 )$; endpoints of latus rectum: $( - 12 , - 3 ) ; ( 12 , - 3 )$ 
B)  focus: $( 0,3 )$; endpoints of latus rectum: $( - 12,3 ) ; ( 12,3 )$ 
C)  focus: $( 0 , - 3 )$; endpoints of latus rectum: $( - 6 , - 3 ) ; ( 6 , - 3 )$ 
D)  focus: $( 0,3 )$; endpoints of latus rectum: $( - 6,3 ) ; ( 6,3 )$

Question 11

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-If the line of symmetry is horizontal, then the parabola opens (horizontally/vertically).

Accepted Answer

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

When referring to the standard form of an equation of an ellipse, the________ , e, is defined as $e = \frac { \square } { \square }$

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the focus and the equation of the directrix. - $4 x ^ { 2 } + 28 x + 40 y + 209 = 0$

Write the standard form of an equation of the ellipse subject to the given conditions. -Center $( 0,0 )$ ; Eccentricity: $\frac { 24 } { 25 }$ ; Major axis vertical of length 50 units

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the vertex and the equation of the directrix. - $y ^ { 2 } + 16 x - 4 y + 52 = 0$

Graph the ellipse. Identify the foci and vertices. - $25 ( x + 2 ) ^ { 2 } + 9 ( x + 4 ) ^ { 2 } = 225$

Determine the standard form of an equation of the parabola subject to the given conditions. -Vertex: $( - 1 , - 3 )$ ; Directrix: $x = - 5$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -When referring to the standard form of an equation of a hyperbola, the________ , e, is defined as e $= \frac { \square } { \square }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The midpoint of the transverse axis is the ________of the hyperbola.

An equation of a parabola $( y - k ) ^ { 2 } = 4 p ( x - h )$ is given. Graph the parabola. Write the equation for the directrix and axis of symmetry. - $( y - 1 ) ^ { 2 } = 12 ( x - 2 )$

An equation of the form $x ^ { 2 } = 4 p y$ is given. Identify the focus and the endpoints of the latus rectum. - $x ^ { 2 } = - 12 y$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the line of symmetry is horizontal, then the parabola opens (horizontally/vertically).

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Exam 7: Analytic Geometry

When referring to the standard form of an equation of an ellipse, the________ , e, is defined as e=□□e = \frac { \square } { \square }e=□□​

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the focus and the equation of the directrix. - 4x2+28x+40y+209=04 x ^ { 2 } + 28 x + 40 y + 209 = 04x2+28x+40y+209=0

Write the standard form of an equation of the ellipse subject to the given conditions. -Center (0,0)( 0,0 )(0,0) ; Eccentricity: 2425\frac { 24 } { 25 }2524​ ; Major axis vertical of length 50 units

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the vertex and the equation of the directrix. - y2+16x−4y+52=0y ^ { 2 } + 16 x - 4 y + 52 = 0y2+16x−4y+52=0

Graph the ellipse. Identify the foci and vertices. - 25(x+2)2+9(x+4)2=22525 ( x + 2 ) ^ { 2 } + 9 ( x + 4 ) ^ { 2 } = 22525(x+2)2+9(x+4)2=225

Determine the standard form of an equation of the parabola subject to the given conditions. -Vertex: (−1,−3)( - 1 , - 3 )(−1,−3) ; Directrix: x=−5x = - 5x=−5

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -When referring to the standard form of an equation of a hyperbola, the________ , e, is defined as e =□□= \frac { \square } { \square }=□□​

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The midpoint of the transverse axis is the ________of the hyperbola.

An equation of a parabola (y−k)2=4p(x−h)( y - k ) ^ { 2 } = 4 p ( x - h )(y−k)2=4p(x−h) is given. Graph the parabola. Write the equation for the directrix and axis of symmetry. - (y−1)2=12(x−2)( y - 1 ) ^ { 2 } = 12 ( x - 2 )(y−1)2=12(x−2)

An equation of the form x2=4pyx ^ { 2 } = 4 p yx2=4py is given. Identify the focus and the endpoints of the latus rectum. - x2=−12yx ^ { 2 } = - 12 yx2=−12y

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the line of symmetry is horizontal, then the parabola opens (horizontally/vertically).

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

When referring to the standard form of an equation of an ellipse, the________ , e, is defined as $e = \frac { \square } { \square }$

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the focus and the equation of the directrix. - $4 x ^ { 2 } + 28 x + 40 y + 209 = 0$

Write the standard form of an equation of the ellipse subject to the given conditions. -Center $( 0,0 )$ ; Eccentricity: $\frac { 24 } { 25 }$ ; Major axis vertical of length 50 units

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the vertex and the equation of the directrix. - $y ^ { 2 } + 16 x - 4 y + 52 = 0$

Graph the ellipse. Identify the foci and vertices. - $25 ( x + 2 ) ^ { 2 } + 9 ( x + 4 ) ^ { 2 } = 225$

Determine the standard form of an equation of the parabola subject to the given conditions. -Vertex: $( - 1 , - 3 )$ ; Directrix: $x = - 5$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -When referring to the standard form of an equation of a hyperbola, the________ , e, is defined as e $= \frac { \square } { \square }$

An equation of a parabola $( y - k ) ^ { 2 } = 4 p ( x - h )$ is given. Graph the parabola. Write the equation for the directrix and axis of symmetry. - $( y - 1 ) ^ { 2 } = 12 ( x - 2 )$

An equation of the form $x ^ { 2 } = 4 p y$ is given. Identify the focus and the endpoints of the latus rectum. - $x ^ { 2 } = - 12 y$