Question 1

Find the standard form of the equation of the ellipse with the following characteristics. focies: (±8,0)major axis of length: 22

Accepted Answer

A)  $$\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 64 } = 1$$ 
B) ​ $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 64 } = 1$ 
C)  $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 57 } = 1$ 
D)  $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 420 } = 1$ 
E)  $$\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 121 } = 1$$ 
A)  $$\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 64 } = 1$$ 
B) ​ $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 64 } = 1$ 
C)  $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 57 } = 1$ 
D)  $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 420 } = 1$ 
E)  $$\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 121 } = 1$$

Question 2

Find the vertex and focus of the parabola. $( y - 3 ) ^ { 2 } + 8 ( x + 6 ) = 0$

Accepted Answer

A) vertex: $( 6 , - 3 )$ focus: $$( 6,5 )$$ 
B) vertex: $( 6 , - 3 )$ focus: $$( 6 , - 11 )$$ 
C) vertex: $( 6 , - 3 )$ focus: $( 4 , - 3 )$ 
D) vertex: $( - 6,3 )$ focus: $( - 8,3 )$ 
E) vertex: $( - 6,3 )$ focus: $( - 6 , - 3 )$ 
A) vertex: $( 6 , - 3 )$ focus: $$( 6,5 )$$ 
B) vertex: $( 6 , - 3 )$ focus: $$( 6 , - 11 )$$ 
C) vertex: $( 6 , - 3 )$ focus: $( 4 , - 3 )$ 
D) vertex: $( - 6,3 )$ focus: $( - 8,3 )$ 
E) vertex: $( - 6,3 )$ focus: $( - 6 , - 3 )$

Question 3

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Focus: (-4,0)
​

Accepted Answer

A)  $y ^ { 2 } = - 16 x$ 
B)  $$y ^ { 2 } = 16 x$$ 
C)  $$x ^ { 2 } = - 16 y$$ 
D)  $x ^ { 2 } = - 16 y$ 
E)  $y ^ { 2 } = - \frac { x } { 16 }$ 
A)  $y ^ { 2 } = - 16 x$ 
B)  $$y ^ { 2 } = 16 x$$ 
C)  $$x ^ { 2 } = - 16 y$$ 
D)  $x ^ { 2 } = - 16 y$ 
E)  $y ^ { 2 } = - \frac { x } { 16 }$

Question 4

Find the vertex and focus of the parabola from the given equation and select its graph.​ $$x ^ { 2 } + 16 y = 0$$ ​

Accepted Answer

A) Vertex: (0,0) Focus: (4,0)   
B) Vertex: (0,0) Focus: (-4,0)   
C) Vertex: (0,-4) Focus: (0,0)   
D) Vertex: (0,0) Focus: (0,4)   
E) Vertex: (0,0) Focus: (0,-4)   
A) Vertex: (0,0) Focus: (4,0)   
B) Vertex: (0,0) Focus: (-4,0)   
C) Vertex: (0,-4) Focus: (0,0)   
D) Vertex: (0,0) Focus: (0,4)   
E) Vertex: (0,0) Focus: (0,-4)

Question 5

Find the center and vertices of the hyperbola and select its graph,using asymptotes as sketching aids.​ $4 y ^ { 2 } - 25 x ^ { 2 } = 100$ ​

Accepted Answer

A) Centre: (0,0) Vertices: (0,-5)   
B) Centre: (0,0) Vertices: (±5,0)   
C) Centre: (0,0) Vertices: (0,±5)   
D) Centre: (0,0) Vertices: (0,5)   
E) Centre: (0,0) Vertices: (5,0)   
A) Centre: (0,0) Vertices: (0,-5)   
B) Centre: (0,0) Vertices: (±5,0)   
C) Centre: (0,0) Vertices: (0,±5)   
D) Centre: (0,0) Vertices: (0,5)   
E) Centre: (0,0) Vertices: (5,0)

Question 6

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Passes through the point $\left( - 5 , \frac { 1 } { 3 } \right)$ ;vertical axis
​

Accepted Answer

A)  $x ^ { 2 } = 75 y$ 
B)  $x ^ { 2 } = - 75 y$ 
C)  $y ^ { 2 } = - 75 x$ 
D)  $y ^ { 2 } = 75 x$ 
E)  $x ^ { 2 } = \frac { y } { 75 }$ 
A)  $x ^ { 2 } = 75 y$ 
B)  $x ^ { 2 } = - 75 y$ 
C)  $y ^ { 2 } = - 75 x$ 
D)  $y ^ { 2 } = 75 x$ 
E)  $x ^ { 2 } = \frac { y } { 75 }$

Question 7

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Focus: (0,-2)
​

Accepted Answer

A)  $y ^ { 2 } = 8 x$ 
B)  $x ^ { 2 } = - 8 y$ 
C)  $y ^ { 2 } = - 8 x$ 
D)  $x ^ { 2 } = 8 y$ 
E)  $x ^ { 2 } = - \frac { y } { 8 }$ 
A)  $y ^ { 2 } = 8 x$ 
B)  $x ^ { 2 } = - 8 y$ 
C)  $y ^ { 2 } = - 8 x$ 
D)  $x ^ { 2 } = 8 y$ 
E)  $x ^ { 2 } = - \frac { y } { 8 }$

Question 8

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.​ $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 49 } = 1$ ​

Accepted Answer

A) Center: (0,0) Vertices: (±10,0)
​   
B) Center: (0,0) Vertices: (10,0)   
C) Center: (0,0) Vertices: (-10,0)
​   
D) Center: (0,0) Vertices: (-10,0)
​   
E) Center: (0,0) Vertices: (±10,0)
​   
A) Center: (0,0) Vertices: (±10,0)
​   
B) Center: (0,0) Vertices: (10,0)   
C) Center: (0,0) Vertices: (-10,0)
​   
D) Center: (0,0) Vertices: (-10,0)
​   
E) Center: (0,0) Vertices: (±10,0)
​

Question 9

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Directrix: y = -1
​

Accepted Answer

A)  $y ^ { 2 } = 4 x$ 
B)  $x ^ { 2 } = - \frac { y } { 4 }$ 
C)  $x ^ { 2 } = 4 y$ 
D)  $y ^ { 2 } = - 4 x$ 
E)  $x ^ { 2 } = - 4 y$ 
A)  $y ^ { 2 } = 4 x$ 
B)  $x ^ { 2 } = - \frac { y } { 4 }$ 
C)  $x ^ { 2 } = 4 y$ 
D)  $y ^ { 2 } = - 4 x$ 
E)  $x ^ { 2 } = - 4 y$

Question 10

Find the standard form of the equation of the parabola with the given characteristics. ​
Vertex: $( 6,5 )$ ;focus: $( 8,5 )$ ​

Accepted Answer

A)  $( y - 6 ) ^ { 2 } = 8 ( x - 5 )$ 
B)  $( y - 5 ) ^ { 2 } = 8 ( x - 6 )$ 
C)  $( x - 6 ) ^ { 2 } = - 8 ( y - 5 )$ 
D)  $( y - 6 ) ^ { 2 } = - 8 ( x - 5 )$ 
E)  $( x - 5 ) ^ { 2 } = 8 ( y - 6 )$ 
A)  $( y - 6 ) ^ { 2 } = 8 ( x - 5 )$ 
B)  $( y - 5 ) ^ { 2 } = 8 ( x - 6 )$ 
C)  $( x - 6 ) ^ { 2 } = - 8 ( y - 5 )$ 
D)  $( y - 6 ) ^ { 2 } = - 8 ( x - 5 )$ 
E)  $( x - 5 ) ^ { 2 } = 8 ( y - 6 )$

Question 11

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Focus: (0, $\frac { 1 } { 2 }$ )
​

Accepted Answer

A)  $y ^ { 2 } = - 2 x$ 
B)  $x ^ { 2 } = - 2 y$ ​ 
C)  $y ^ { 2 } = 2 x$ 
D)  $x ^ { 2 } = 2 y$ 
E)  $x ^ { 2 } = \frac { y } { 2 }$ 
A)  $y ^ { 2 } = - 2 x$ 
B)  $x ^ { 2 } = - 2 y$ ​ 
C)  $y ^ { 2 } = 2 x$ 
D)  $x ^ { 2 } = 2 y$ 
E)  $x ^ { 2 } = \frac { y } { 2 }$

Question 12

Give the coordinates of the circle's center and it radius.​ $$( x - 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 1$$ ​
Enter your answer using the coordinate notation: (a,b),and r = ....separated with a comma.

Accepted Answer

The answer of Give the coordinates of the circle's center...

Question 13

The revenue (in dollars)generated by the sale of units of a patio furniture set is given by $$( x - 130 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 23,660 )$$ .Select the correct graph of the function. ​

Accepted Answer

A) ​   . 
B) ​   
C) ​   
D) ​   
E) ​   ​ 
A) ​   . 
B) ​   
C) ​   
D) ​   
E) ​   ​

Question 14

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Directrix: y = 2
​

Accepted Answer

A)  $x ^ { 2 } = - 8 y$ 
B)  $x ^ { 2 } = 8 y$ 
C)  $y ^ { 2 } = - 8 x$ 
D)  $y ^ { 2 } = 8 x$ 
E)  $x ^ { 2 } = - \frac { y } { 8 }$ 
A)  $x ^ { 2 } = - 8 y$ 
B)  $x ^ { 2 } = 8 y$ 
C)  $y ^ { 2 } = - 8 x$ 
D)  $y ^ { 2 } = 8 x$ 
E)  $x ^ { 2 } = - \frac { y } { 8 }$

Question 15

Use a graphing utility to graph the parabola. $$y = x ^ { 2 } + 4 x - 2$$ ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 16

Match the equation with its graph. $x ^ { 2 } + 4 y ^ { 2 } = 4$

Accepted Answer

A)    
B)    
C)    ​ 
D)    
E)    ​ 
A)    
B)    
C)    ​ 
D)    
E)    ​

Question 17

Select the standard form of the equation of the parabola and determine the coordinates of the focus. ​​   ​

Accepted Answer

A)  $y ^ { 2 } = - \frac { 49 } { 5 } x$ ;Focus: $\left( \frac { 49 } { 20 } , 0 \right)$ 
B)  $y ^ { 2 } = \frac { 49 } { 5 } x$ ;Focus: $\left( \frac { 49 } { 20 } , 0 \right)$ 
C)  $y ^ { 2 } = - \frac { 49 } { 5 } x$ ;Focus: $\left( - \frac { 49 } { 20 } , 0 \right)$ 
D)  $x ^ { 2 } = - \frac { 49 } { 5 } y$ Focus: $\left( \frac { 49 } { 20 } , 0 \right)$ 
E)  $x ^ { 2 } = \frac { 49 } { 5 } y$ ;Focus: $\left( \frac { 49 } { 20 } , 0 \right)$ 
A)  $y ^ { 2 } = - \frac { 49 } { 5 } x$ ;Focus: $\left( \frac { 49 } { 20 } , 0 \right)$ 
B)  $y ^ { 2 } = \frac { 49 } { 5 } x$ ;Focus: $\left( \frac { 49 } { 20 } , 0 \right)$ 
C)  $y ^ { 2 } = - \frac { 49 } { 5 } x$ ;Focus: $\left( - \frac { 49 } { 20 } , 0 \right)$ 
D)  $x ^ { 2 } = - \frac { 49 } { 5 } y$ Focus: $\left( \frac { 49 } { 20 } , 0 \right)$ 
E)  $x ^ { 2 } = \frac { 49 } { 5 } y$ ;Focus: $\left( \frac { 49 } { 20 } , 0 \right)$

Question 18

Find the vertex,focus,and directrix of the parabola.​ $( x + 5 ) ^ { 2 } = 4 \left( y - \frac { 5 } { 2 } \right)$ ​

Accepted Answer

A) Vertex: $\left( - 5 , \frac { 5 } { 2 } \right)$ ;Focus: $\left( - 5 , \frac { 7 } { 2 } \right)$ ;Directrix: $y = \frac { 3 } { 2 }$ 
B) Vertex: $\left( \frac { 5 } { 2 } , - 5 \right)$ ;Focus: $\left( - 5 , \frac { 3 } { 2 } \right)$ ;Directrix: $y = \frac { 3 } { 2 }$ 
C) Vertex: $\left( \frac { 5 } { 2 } , - 5 \right)$ ;Focus: $\left( - 5 , \frac { 7 } { 2 } \right)$ ;Directrix: $y = \frac { 3 } { 2 }$ 
D) Vertex: $\left( - 5 , \frac { 5 } { 2 } \right)$ ;Focus: $\left( - 5 , \frac { 3 } { 2 } \right)$ ;Directrix: $y = \frac { 7 } { 2 }$ 
E) Vertex: $( 0,0 )$ ;Focus: $\left( - 5 , \frac { 7 } { 2 } \right)$ ;Directrix: $y = \frac { 7 } { 2 }$ 
A) Vertex: $\left( - 5 , \frac { 5 } { 2 } \right)$ ;Focus: $\left( - 5 , \frac { 7 } { 2 } \right)$ ;Directrix: $y = \frac { 3 } { 2 }$ 
B) Vertex: $\left( \frac { 5 } { 2 } , - 5 \right)$ ;Focus: $\left( - 5 , \frac { 3 } { 2 } \right)$ ;Directrix: $y = \frac { 3 } { 2 }$ 
C) Vertex: $\left( \frac { 5 } { 2 } , - 5 \right)$ ;Focus: $\left( - 5 , \frac { 7 } { 2 } \right)$ ;Directrix: $y = \frac { 3 } { 2 }$ 
D) Vertex: $\left( - 5 , \frac { 5 } { 2 } \right)$ ;Focus: $\left( - 5 , \frac { 3 } { 2 } \right)$ ;Directrix: $y = \frac { 7 } { 2 }$ 
E) Vertex: $( 0,0 )$ ;Focus: $\left( - 5 , \frac { 7 } { 2 } \right)$ ;Directrix: $y = \frac { 7 } { 2 }$

Question 19

As a speeding train crosses a trestle over a deep gorge,a child drops his toy plane from the window.The path of the toy plane is modeled by $x ^ { 2 } = - 6.0 ( y - 110 )$ ,where y is the height above the floor of the gorge and distances are measured in feet.How far will the toy plane travel horizontally before it hits the bottom of the gorge? [Note: The toy plane does not glide;it "drops like a rock."]

Accepted Answer

A) 6.0 ft 
B) 10 ft 
C) 25.7 ft 
D) 110 ft 
E) 660.0 ft 
A) 6.0 ft 
B) 10 ft 
C) 25.7 ft 
D) 110 ft 
E) 660.0 ft

Question 20

A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 20 feet and a height at the center of 4 feet.Select the arch of the tunnel on a rectangular coordinate system with the center of the road entering the tunnel at the origin.Identify the coordinates of the known points. ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Exam 60: Introduction to Conics Parabolas

Find the standard form of the equation of the ellipse with the following characteristics. focies: (±8,0)major axis of length: 22

Find the vertex and focus of the parabola. (y−3)2+8(x+6)=0( y - 3 ) ^ { 2 } + 8 ( x + 6 ) = 0(y−3)2+8(x+6)=0

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​ Focus: (-4,0) ​

Find the vertex and focus of the parabola from the given equation and select its graph.​ x2+16y=0x ^ { 2 } + 16 y = 0x2+16y=0 ​

Find the center and vertices of the hyperbola and select its graph,using asymptotes as sketching aids.​ 4y2−25x2=1004 y ^ { 2 } - 25 x ^ { 2 } = 1004y2−25x2=100 ​

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​ Passes through the point (−5,13)\left( - 5 , \frac { 1 } { 3 } \right)(−5,31​) ;vertical axis ​

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​ Focus: (0,-2) ​

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.​ x2100+y249=1\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 49 } = 1100x2​+49y2​=1 ​

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​ Directrix: y = -1 ​

Find the standard form of the equation of the parabola with the given characteristics. ​ Vertex: (6,5)( 6,5 )(6,5) ;focus: (8,5)( 8,5 )(8,5) ​

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​ Focus: (0, 12\frac { 1 } { 2 }21​ ) ​

Give the coordinates of the circle's center and it radius.​ (x−4)2+(y+3)2=1( x - 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 1(x−4)2+(y+3)2=1 ​ Enter your answer using the coordinate notation: (a,b),and r = ....separated with a comma.

The revenue (in dollars)generated by the sale of units of a patio furniture set is given by (x−130)2=−57(R−23,660)( x - 130 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 23,660 )(x−130)2=−75​(R−23,660) .Select the correct graph of the function. ​

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​ Directrix: y = 2 ​

Use a graphing utility to graph the parabola. y=x2+4x−2y = x ^ { 2 } + 4 x - 2y=x2+4x−2 ​

Match the equation with its graph. x2+4y2=4x ^ { 2 } + 4 y ^ { 2 } = 4x2+4y2=4

Select the standard form of the equation of the parabola and determine the coordinates of the focus. ​​ ​

Find the vertex,focus,and directrix of the parabola.​ (x+5)2=4(y−52)( x + 5 ) ^ { 2 } = 4 \left( y - \frac { 5 } { 2 } \right)(x+5)2=4(y−25​) ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Ellipses

Hyperbolas

Find the vertex and focus of the parabola. $( y - 3 ) ^ { 2 } + 8 ( x + 6 ) = 0$

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. Focus: (-4,0)

Find the vertex and focus of the parabola from the given equation and select its graph. $x ^ { 2 } + 16 y = 0$

Find the center and vertices of the hyperbola and select its graph,using asymptotes as sketching aids. $4 y ^ { 2 } - 25 x ^ { 2 } = 100$

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. Passes through the point $\left( - 5 , \frac { 1 } { 3 } \right)$ ;vertical axis

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. Focus: (0,-2)

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph. $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 49 } = 1$

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. Directrix: y = -1

Find the standard form of the equation of the parabola with the given characteristics. Vertex: $( 6,5 )$ ;focus: $( 8,5 )$

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. Focus: (0, $\frac { 1 } { 2 }$ )

Give the coordinates of the circle's center and it radius. $( x - 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 1$ Enter your answer using the coordinate notation: (a,b),and r = ....separated with a comma.

The revenue (in dollars)generated by the sale of units of a patio furniture set is given by $( x - 130 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 23,660 )$ .Select the correct graph of the function.

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. Directrix: y = 2

Use a graphing utility to graph the parabola. $y = x ^ { 2 } + 4 x - 2$

Match the equation with its graph. $x ^ { 2 } + 4 y ^ { 2 } = 4$

Select the standard form of the equation of the parabola and determine the coordinates of the focus.

Find the vertex,focus,and directrix of the parabola. $( x + 5 ) ^ { 2 } = 4 \left( y - \frac { 5 } { 2 } \right)$