Question 1

Identify the conic and select its correct graph.​ $$r = \frac { 2 } { 2 + 3 \sin \theta }$$ ​

Accepted Answer

A)  $$e = \frac { 3 } { 2 } > 1 \Rightarrow$$ Hyperbola ​  
​ 
B)  $$e = \frac { 3 } { 2 } > 1 \Rightarrow$$ Hyperbola   ​
​ 
C)  $$e = \frac { 3 } { 2 } > 1 \Rightarrow$$ Hyperbola ​   
D)  $$e = \frac { 3 } { 2 } > 1 \Rightarrow$$ Hyperbola ​   
E)  $$e = \frac { 3 } { 2 } > 1 \Rightarrow$$ Hyperbola ​   
A)  $$e = \frac { 3 } { 2 } > 1 \Rightarrow$$ Hyperbola ​  
​ 
B)  $$e = \frac { 3 } { 2 } > 1 \Rightarrow$$ Hyperbola   ​
​ 
C)  $$e = \frac { 3 } { 2 } > 1 \Rightarrow$$ Hyperbola ​   
D)  $$e = \frac { 3 } { 2 } > 1 \Rightarrow$$ Hyperbola ​   
E)  $$e = \frac { 3 } { 2 } > 1 \Rightarrow$$ Hyperbola ​

Question 2

Find a polar equation of the conic with its focus at the pole. ​
Conics
Vertex or vertices
Parabola $( 4,0 )$ ​

Accepted Answer

A)  $\frac { 8 } { 1 - \cos \theta }$ 
B)  $\frac { 8 } { 1 - \sin \theta }$ 
C)  $\frac { - 8 } { 1 - \sin \theta }$ 
D)  $\frac { 8 } { 1 + \sin \theta }$ 
E)  $\frac { 8 } { 1 + \cos \theta }$ 
A)  $\frac { 8 } { 1 - \cos \theta }$ 
B)  $\frac { 8 } { 1 - \sin \theta }$ 
C)  $\frac { - 8 } { 1 - \sin \theta }$ 
D)  $\frac { 8 } { 1 + \sin \theta }$ 
E)  $\frac { 8 } { 1 + \cos \theta }$

Question 3

Select the polar equation of graph.​   ​

Accepted Answer

A)  $\frac { 6 } { 2 - \cos \theta }$ 
B)  $$\frac { 6 } { 2 - \sin \theta }$$ 
C)  $$\frac { 1 } { 2 - \cos \theta }$$ 
D)  $\frac { 6 } { 2 + \sin \theta }$ 
E)  $\frac { 6 } { 2 + \cos \theta }$ 
A)  $\frac { 6 } { 2 - \cos \theta }$ 
B)  $$\frac { 6 } { 2 - \sin \theta }$$ 
C)  $$\frac { 1 } { 2 - \cos \theta }$$ 
D)  $\frac { 6 } { 2 + \sin \theta }$ 
E)  $\frac { 6 } { 2 + \cos \theta }$

Question 4

Consider the polar equation:​ $r = \frac { 8 } { 1 - 0.4 \cos \theta }$ ​ Identify the conic without graphing the equation.
​

Accepted Answer

A)  $e < 1$ ,the conic is a parabola. 
B)  $e < 1$ ,the conic is a circle. 
C)  $e < 1$ ,the conic is a hyperbola. 
D)  $e < 1$ ,the conic is an ellipse. 
E) None of the above 
A)  $e < 1$ ,the conic is a parabola. 
B)  $e < 1$ ,the conic is a circle. 
C)  $e < 1$ ,the conic is a hyperbola. 
D)  $e < 1$ ,the conic is an ellipse. 
E) None of the above

Question 5

Use the following results the polar equation of the hyperbolla $\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ is $r ^ { 2 } = \frac { - b ^ { 2 } } { 1 - e ^ { 2 } \cos ^ { 2 } \theta }$ to write the polar form of the equation of the conic $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ . ​

Accepted Answer

A)  $r ^ { 2 } = \frac { 144 } { 16 \cos ^ { 2 } \theta + 25 }$ 
B)  $r ^ { 2 } = \frac { 144 } { 25 \cos ^ { 2 } \theta - 16 }$ 
C)  $r ^ { 2 } = \frac { 144 } { 25 \cos ^ { 2 } \theta + 16 }$ 
D)  $r ^ { 2 } = \frac { - 144 } { 25 \cos ^ { 2 } \theta + 16 }$ 
E)  $r ^ { 2 } = \frac { 144 } { 16 - 25 \cos ^ { 2 } \theta }$ 
A)  $r ^ { 2 } = \frac { 144 } { 16 \cos ^ { 2 } \theta + 25 }$ 
B)  $r ^ { 2 } = \frac { 144 } { 25 \cos ^ { 2 } \theta - 16 }$ 
C)  $r ^ { 2 } = \frac { 144 } { 25 \cos ^ { 2 } \theta + 16 }$ 
D)  $r ^ { 2 } = \frac { - 144 } { 25 \cos ^ { 2 } \theta + 16 }$ 
E)  $r ^ { 2 } = \frac { 144 } { 16 - 25 \cos ^ { 2 } \theta }$

Question 6

By using a graphing utility select the correct graph of the polar equation.​ $$\frac { - 3 } { 1 - \sin \theta }$$ ​

Accepted Answer

A) ​   $$e = 1 \Rightarrow \text { Parabola }$$ ​ 
B) ​   $$e = 1 \Rightarrow \text { Parabola }$$ 
C) ​   $$e = 1 \Rightarrow \text { Parabola }$$ 
D) ​   $$e = 1 \Rightarrow \text { Parabola }$$ 
E) ​   $$e = 1 \Rightarrow \text { Parabola }$$ 
A) ​   $$e = 1 \Rightarrow \text { Parabola }$$ ​ 
B) ​   $$e = 1 \Rightarrow \text { Parabola }$$ 
C) ​   $$e = 1 \Rightarrow \text { Parabola }$$ 
D) ​   $$e = 1 \Rightarrow \text { Parabola }$$ 
E) ​   $$e = 1 \Rightarrow \text { Parabola }$$

Question 7

Identify the conic and select its correct graph.​ $$r = \frac { 4 } { 2 + 8 \sin \theta }$$ ​

Accepted Answer

A)  $$e = 4 > 1 \Rightarrow$$ Hyperbola ​  
​ 
B)  $$e = 4 > 1 \Rightarrow$$ Hyperbola ​   
C)  $$e = 4 > 1 \Rightarrow$$ Hyperbola ​   
D)  $$e = 4 > 1 \Rightarrow$$ Hyperbola ​  
​
​ 
E)  $$e = 4 > 1 \Rightarrow$$ Hyperbola ​   
A)  $$e = 4 > 1 \Rightarrow$$ Hyperbola ​  
​ 
B)  $$e = 4 > 1 \Rightarrow$$ Hyperbola ​   
C)  $$e = 4 > 1 \Rightarrow$$ Hyperbola ​   
D)  $$e = 4 > 1 \Rightarrow$$ Hyperbola ​  
​
​ 
E)  $$e = 4 > 1 \Rightarrow$$ Hyperbola ​

Question 8

Select the polar equation of graph.​   ​

Accepted Answer

A)  $$\frac { 1 } { 1 - \cos \theta }$$ 
B)  $$\frac { 4 } { 1 - \sin \theta }$$ 
C)  $$\frac { 4 } { 1 + \sin \theta }$$ 
D)  $$\frac { 4 } { 1 - \cos \theta }$$ 
E)  $$\frac { 4 } { 1 + \cos \theta }$$ 
A)  $$\frac { 1 } { 1 - \cos \theta }$$ 
B)  $$\frac { 4 } { 1 - \sin \theta }$$ 
C)  $$\frac { 4 } { 1 + \sin \theta }$$ 
D)  $$\frac { 4 } { 1 - \cos \theta }$$ 
E)  $$\frac { 4 } { 1 + \cos \theta }$$

Question 9

Select the polar equation of the conic for ​e = 1.0 and identify the conic for the following equation.​ $r = \frac { 2 e } { 1 + e \sin \theta }$ ​

Accepted Answer

A)  $r = \frac { 1 } { 1 + \sin \theta } \Rightarrow \text { parabola }$ 
B)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$ 
C)  $r = \frac { 2 } { 1 - 2 \sin \theta } \Rightarrow \text { ellipse }$ 
D)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { ellipse }$ 
E)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$ 
A)  $r = \frac { 1 } { 1 + \sin \theta } \Rightarrow \text { parabola }$ 
B)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$ 
C)  $r = \frac { 2 } { 1 - 2 \sin \theta } \Rightarrow \text { ellipse }$ 
D)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { ellipse }$ 
E)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$

Question 10

Select correct graph to graph rotated conic.​ $$r = \frac { 6 } { 6 + \sin ( \theta - \pi / 3 ) }$$ ​

Accepted Answer

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

Exam 66: Polar Equations of Conics

Identify the conic and select its correct graph.​ r=22+3sin⁡θr = \frac { 2 } { 2 + 3 \sin \theta }r=2+3sinθ2​ ​

Find a polar equation of the conic with its focus at the pole. ​ Conics Vertex or vertices Parabola (4,0)( 4,0 )(4,0) ​

Select the polar equation of graph.​ ​

Consider the polar equation:​ r=81−0.4cos⁡θr = \frac { 8 } { 1 - 0.4 \cos \theta }r=1−0.4cosθ8​ ​ Identify the conic without graphing the equation. ​

By using a graphing utility select the correct graph of the polar equation.​ −31−sin⁡θ\frac { - 3 } { 1 - \sin \theta }1−sinθ−3​ ​

Identify the conic and select its correct graph.​ r=42+8sin⁡θr = \frac { 4 } { 2 + 8 \sin \theta }r=2+8sinθ4​ ​

Select the polar equation of graph.​ ​

Select the polar equation of the conic for ​e = 1.0 and identify the conic for the following equation.​ r=2e1+esin⁡θr = \frac { 2 e } { 1 + e \sin \theta }r=1+esinθ2e​ ​

Select correct graph to graph rotated conic.​ r=66+sin⁡(θ−π/3)r = \frac { 6 } { 6 + \sin ( \theta - \pi / 3 ) }r=6+sin(θ−π/3)6​ ​

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

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Polar Coordinates

Graphs of Polar Equations

Filters

Identify the conic and select its correct graph. $r = \frac { 2 } { 2 + 3 \sin \theta }$

Find a polar equation of the conic with its focus at the pole. Conics Vertex or vertices Parabola $( 4,0 )$

Select the polar equation of graph.

Consider the polar equation: $r = \frac { 8 } { 1 - 0.4 \cos \theta }$ Identify the conic without graphing the equation.

By using a graphing utility select the correct graph of the polar equation. $\frac { - 3 } { 1 - \sin \theta }$

Identify the conic and select its correct graph. $r = \frac { 4 } { 2 + 8 \sin \theta }$

Select the polar equation of graph.

Select the polar equation of the conic for e = 1.0 and identify the conic for the following equation. $r = \frac { 2 e } { 1 + e \sin \theta }$

Select correct graph to graph rotated conic. $r = \frac { 6 } { 6 + \sin ( \theta - \pi / 3 ) }$