Question 1

Find the equation of the circle graphed below.​   ​

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } = 6$ 
B)  $$y ^ { 2 } = x ^ { 2 } + 36$$ 
C)  $$x ^ { 2 } + y ^ { 2 } = 36$$ 
D)  $x ^ { 2 } + y ^ { 2 } = 1$ 
E)  $x ^ { 2 } + y = 36$ 
A)  $x ^ { 2 } + y ^ { 2 } = 6$ 
B)  $$y ^ { 2 } = x ^ { 2 } + 36$$ 
C)  $$x ^ { 2 } + y ^ { 2 } = 36$$ 
D)  $x ^ { 2 } + y ^ { 2 } = 1$ 
E)  $x ^ { 2 } + y = 36$

Question 2

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.​ $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 1 / 9 } = 1$ ​

Accepted Answer

A) Center: (0,0) Vertices: (±3,0)   
B) Center: (0,0) Vertices: (-3,0)   
C) Center: (0,0) Vertices: (3,0)
​   
D) Center: (0,0) Vertices: (±3,0)
​   
E) Center: (0,0) Vertices: (-3,0)
​   
A) Center: (0,0) Vertices: (±3,0)   
B) Center: (0,0) Vertices: (-3,0)   
C) Center: (0,0) Vertices: (3,0)
​   
D) Center: (0,0) Vertices: (±3,0)
​   
E) Center: (0,0) Vertices: (-3,0)
​

Question 3

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

Accepted Answer

A)  $x ^ { 2 } = - 3 y$ focus: $$\left( 0 , - \frac { 1 } { 3 } \right)$$ 
B)  $$x ^ { 2 } = - \frac { 1 } { 12 } y$$ focus: $$\left( 0 , - \frac { 1 } { 12 } \right)$$ 
C)  $$x ^ { 2 } = - 3 y$$ focus: (0,- 4) 
D)  $x ^ { 2 } = - \frac { 1 } { 3 } y$ focus: $\left( 0 , - \frac { 1 } { 3 } \right)$ 
E)  $x ^ { 2 } = - \frac { 1 } { 3 } y$ focus: $\left( 0 , - \frac { 1 } { 12 } \right)$ 
A)  $x ^ { 2 } = - 3 y$ focus: $$\left( 0 , - \frac { 1 } { 3 } \right)$$ 
B)  $$x ^ { 2 } = - \frac { 1 } { 12 } y$$ focus: $$\left( 0 , - \frac { 1 } { 12 } \right)$$ 
C)  $$x ^ { 2 } = - 3 y$$ focus: (0,- 4) 
D)  $x ^ { 2 } = - \frac { 1 } { 3 } y$ focus: $\left( 0 , - \frac { 1 } { 3 } \right)$ 
E)  $x ^ { 2 } = - \frac { 1 } { 3 } y$ focus: $\left( 0 , - \frac { 1 } { 12 } \right)$

Question 4

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: (0,±3);focies: (0,±7)
​ ​

Accepted Answer

A)  $- \frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 40 } = 1$ 
B)  $\frac { y ^ { 2 } } { 40 } - \frac { x ^ { 2 } } { 9 } = 1$ 
C)  $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 40 } = 1$ 
D)  $\frac { y ^ { 2 } } { 40 } - \frac { x ^ { 2 } } { 9 } = - 1$ 
E)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 40 } = 1$ 
A)  $- \frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 40 } = 1$ 
B)  $\frac { y ^ { 2 } } { 40 } - \frac { x ^ { 2 } } { 9 } = 1$ 
C)  $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 40 } = 1$ 
D)  $\frac { y ^ { 2 } } { 40 } - \frac { x ^ { 2 } } { 9 } = - 1$ 
E)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 40 } = 1$

Question 5

Use a graphing utility to graph the parabola.​ $$x + 5 = 4 ( y - 3 ) ^ { 2 }$$ ​

Accepted Answer

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

Question 6

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0,-1)

Accepted Answer

A) y2 = -4x 
B) x2 = -4y 
C) x2 = y 
D) y2 = -x 
E) x2 = -y 
A) y2 = -4x 
B) x2 = -4y 
C) x2 = y 
D) y2 = -x 
E) x2 = -y

Question 7

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Vertical axis and passes through the point (6,8)
​

Accepted Answer

A)  $x ^ { 2 } = \frac { 36 } { 8 } y$ 
B)  $y ^ { 2 } = \frac { 8 } { 36 } x$ 
C)  $x ^ { 2 } = \frac { 8 } { 36 } y$ 
D)  $y ^ { 2 } = x$ 
E) ​ $y ^ { 2 } = \frac { 36 } { 8 } x$ 
A)  $x ^ { 2 } = \frac { 36 } { 8 } y$ 
B)  $y ^ { 2 } = \frac { 8 } { 36 } x$ 
C)  $x ^ { 2 } = \frac { 8 } { 36 } y$ 
D)  $y ^ { 2 } = x$ 
E) ​ $y ^ { 2 } = \frac { 36 } { 8 } x$

Question 8

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Vertical axis and passes through the point (-8,-8)
​

Accepted Answer

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

Question 9

Find the vertex and focus of the parabola. $( y + 7 ) ^ { 2 } - 16 ( x + 3 ) = 0$

Accepted Answer

A) vertex: $( 3,7 )$ focus: $( 3,7 )$ 
B) vertex: $$( 3,7 )$$ focus: $( - 9 , - 3 )$ 
C) vertex: $$( 3,7 )$$ focus: $( 3,23 )$ 
D) vertex: $( - 3 , - 7 )$ focus: $( - 3 , + 7 )$ 
E) vertex: $( - 3 , - 7 )$ focus: $( 1 , - 7 )$ 
A) vertex: $( 3,7 )$ focus: $( 3,7 )$ 
B) vertex: $$( 3,7 )$$ focus: $( - 9 , - 3 )$ 
C) vertex: $$( 3,7 )$$ focus: $( 3,23 )$ 
D) vertex: $( - 3 , - 7 )$ focus: $( - 3 , + 7 )$ 
E) vertex: $( - 3 , - 7 )$ focus: $( 1 , - 7 )$

Question 10

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: (0,±5);focies: (0,±6)
​

Accepted Answer

A)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 11 } = - 1$ 
B)  $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 11 } = 1$ 
C)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 11 } = 1$ 
D)  $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 11 } = - 1$ 
E)  $- \frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 11 } = - 1$ 
A)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 11 } = - 1$ 
B)  $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 11 } = 1$ 
C)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 11 } = 1$ 
D)  $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 11 } = - 1$ 
E)  $- \frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 11 } = - 1$

Question 11

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

Accepted Answer

A)  $$x ^ { 2 } = \frac { 1 } { 9 } y$$ focus: $\left( 0 , \frac { 1 } { 36 } \right)$ 
B)  $x ^ { 2 } = - \frac { 1 } { 36 } y$ focus: $\left( 0 , - \frac { 1 } { 36 } \right)$ 
C)  $x ^ { 2 } = \frac { 1 } { 9 } y$ focus: $\left( 0 , - \frac { 1 } { 9 } \right)$ 
D)  $x ^ { 2 } = 9 y$ focus: $\left( 0 , - \frac { 1 } { 9 } \right)$ 
E)  $x ^ { 2 } = - 9 y$ focus: (0,4) 
A)  $$x ^ { 2 } = \frac { 1 } { 9 } y$$ focus: $\left( 0 , \frac { 1 } { 36 } \right)$ 
B)  $x ^ { 2 } = - \frac { 1 } { 36 } y$ focus: $\left( 0 , - \frac { 1 } { 36 } \right)$ 
C)  $x ^ { 2 } = \frac { 1 } { 9 } y$ focus: $\left( 0 , - \frac { 1 } { 9 } \right)$ 
D)  $x ^ { 2 } = 9 y$ focus: $\left( 0 , - \frac { 1 } { 9 } \right)$ 
E)  $x ^ { 2 } = - 9 y$ focus: (0,4)

Question 12

Give the coordinates of the circle's center and its radius.​ $$x ^ { 2 } + y ^ { 2 } - 1 = 0$$ ​
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

Use a graphing utility to graph the parabola. $$y = 2 x ^ { 2 } + 4 x - 7$$ ​

Accepted Answer

The answer of Use a graphing utility to graph the...

Question 14

Sketch the graph of the ellipse,using the lateral recta.​ $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$ ​

Accepted Answer

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

Question 15

The revenue R (in dollars)generated by the sale of x units of a patio furniture set is given by $$( x - 112 ) ^ { 2 } = - \frac { 4 } { 5 } ( R - 12544 )$$ .Select the correct graph of the function. ​

Accepted Answer

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

Question 16

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Directrix: x = -4
​

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 17

Identify the conic.​ $4 y ^ { 2 } + 5 x ^ { 2 } - 20 = 0$ ​

Accepted Answer

A) Ellipse 
B) Circle 
C) Parabola 
D) Line 
E) Hyperbola 
A) Ellipse 
B) Circle 
C) Parabola 
D) Line 
E) Hyperbola

Question 18

Find the equation of the parabola with vertex at (0,0)and focus at (0,5). ​

Accepted Answer

A)  $x ^ { 2 } = 20 y$ 
B)  $x ^ { 2 } = 5 y$ 
C)  $y ^ { 2 } = 20 x$ 
D)  $x ^ { 2 } = y + 5$ 
E) none of these 
A)  $x ^ { 2 } = 20 y$ 
B)  $x ^ { 2 } = 5 y$ 
C)  $y ^ { 2 } = 20 x$ 
D)  $x ^ { 2 } = y + 5$ 
E) none of these

Question 19

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Focus: $\left( - \frac { 7 } { 2 } , 0 \right)$ ​

Accepted Answer

A)  $x ^ { 2 } = 14 y$ 
B)  $y ^ { 2 } = - 14 x$ 
C)  $y ^ { 2 } = 14 x$ 
D)  $x ^ { 2 } = - 14 y$ 
E)  $y ^ { 2 } = - \frac { x } { 14 }$ 
A)  $x ^ { 2 } = 14 y$ 
B)  $y ^ { 2 } = - 14 x$ 
C)  $y ^ { 2 } = 14 x$ 
D)  $x ^ { 2 } = - 14 y$ 
E)  $y ^ { 2 } = - \frac { x } { 14 }$

Question 20

In a suspension bridge,the shape of the suspension cables is parabolic.The bridge shown in the figure has towers that are 1000 m apart,and the lowest point of the suspension cables is 200 m below the top of the towers.Find the equation of the parabolic part of the cables,placing the origin of the coordinate system at the lowest point of the cable. ​
NOTE: This equation is used to find the length of the cable needed in the construction of the bridge.​   ​

Accepted Answer

A) x 2 = 2,500y 
B) y 2 = 5,000x 
C) x 2 = 1,250y 
D) x 2 = 5,000y 
E) x 2 = -1,250y 
A) x 2 = 2,500y 
B) y 2 = 5,000x 
C) x 2 = 1,250y 
D) x 2 = 5,000y 
E) x 2 = -1,250y

Exam 60: Introduction to Conics Parabolas

Find the equation of the circle graphed below.​ ​

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.​ x29+y21/9=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 1 / 9 } = 19x2​+1/9y2​=1 ​

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

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​ Vertices: (0,±3);focies: (0,±7) ​ ​

Use a graphing utility to graph the parabola.​ x+5=4(y−3)2x + 5 = 4 ( y - 3 ) ^ { 2 }x+5=4(y−3)2 ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0,-1)

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​ Vertical axis and passes through the point (6,8) ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​ Vertical axis and passes through the point (-8,-8) ​

Find the vertex and focus of the parabola. (y+7)2−16(x+3)=0( y + 7 ) ^ { 2 } - 16 ( x + 3 ) = 0(y+7)2−16(x+3)=0

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​ Vertices: (0,±5);focies: (0,±6) ​

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

Give the coordinates of the circle's center and its radius.​ x2+y2−1=0x ^ { 2 } + y ^ { 2 } - 1 = 0x2+y2−1=0 ​ Enter your answer using the coordinate notation: (a,b)and r = ....separated with a comma.

Use a graphing utility to graph the parabola. y=2x2+4x−7y = 2 x ^ { 2 } + 4 x - 7y=2x2+4x−7 ​

Sketch the graph of the ellipse,using the lateral recta.​ x24+y216=1\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 14x2​+16y2​=1 ​

The revenue R (in dollars)generated by the sale of x units of a patio furniture set is given by (x−112)2=−45(R−12544)( x - 112 ) ^ { 2 } = - \frac { 4 } { 5 } ( R - 12544 )(x−112)2=−54​(R−12544) .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: x = -4 ​

Identify the conic.​ 4y2+5x2−20=04 y ^ { 2 } + 5 x ^ { 2 } - 20 = 04y2+5x2−20=0 ​

Find the equation of the parabola with vertex at (0,0)and focus at (0,5). ​

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​ Focus: (−72,0)\left( - \frac { 7 } { 2 } , 0 \right)(−27​,0) ​

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

Find the equation of the circle graphed below.

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph. $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 1 / 9 } = 1$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±3);focies: (0,±7)

Use a graphing utility to graph the parabola. $x + 5 = 4 ( y - 3 ) ^ { 2 }$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Vertical axis and passes through the point (6,8)

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Vertical axis and passes through the point (-8,-8)

Find the vertex and focus of the parabola. $( y + 7 ) ^ { 2 } - 16 ( x + 3 ) = 0$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±5);focies: (0,±6)

Give the coordinates of the circle's center and its radius. $x ^ { 2 } + y ^ { 2 } - 1 = 0$ Enter your answer using the coordinate notation: (a,b)and r = ....separated with a comma.

Use a graphing utility to graph the parabola. $y = 2 x ^ { 2 } + 4 x - 7$

Sketch the graph of the ellipse,using the lateral recta. $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$

The revenue R (in dollars)generated by the sale of x units of a patio furniture set is given by $( x - 112 ) ^ { 2 } = - \frac { 4 } { 5 } ( R - 12544 )$ .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: x = -4

Identify the conic. $4 y ^ { 2 } + 5 x ^ { 2 } - 20 = 0$

Find the equation of the parabola with vertex at (0,0)and focus at (0,5).

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. Focus: $\left( - \frac { 7 } { 2 } , 0 \right)$