Question 1

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

Accepted Answer

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

Question 2

Find a polar equation of the conic with its focus at the pole. ​
Conics
Eccentricity
Directrix
Hyperbola $e = \frac { 6 } { 5 }$ $x = - 3$ ​

Accepted Answer

A)  $r = \frac { 15 } { 5 - 6 \sin \theta }$ 
B)  $r = \frac { 15 } { 5 - 6 \cos \theta }$ 
C)  $r = \frac { 15 } { 5 + 6 \cos \theta }$ 
D)  $r = \frac { 15 } { 5 + 6 \sin \theta }$ 
E)  $r = \frac { - 15 } { 5 - 6 \cos \theta }$ 
A)  $r = \frac { 15 } { 5 - 6 \sin \theta }$ 
B)  $r = \frac { 15 } { 5 - 6 \cos \theta }$ 
C)  $r = \frac { 15 } { 5 + 6 \cos \theta }$ 
D)  $r = \frac { 15 } { 5 + 6 \sin \theta }$ 
E)  $r = \frac { - 15 } { 5 - 6 \cos \theta }$

Question 3

By using a graphing utility select the correct graph of the polar equation.Identify the graph.​ $$\frac { 12 } { 2 - \cos \theta }$$ ​

Accepted Answer

A) ​   $$e = \frac { 1 } { 2 } < 1 \Rightarrow$$ Ellipse 
B) ​   $$e = \frac { 1 } { 2 } < 1 \Rightarrow$$ Ellipse 
C) ​   $$e = \frac { 1 } { 2 } < 1 \Rightarrow$$ Ellipse 
D) ​   $$e = \frac { 1 } { 2 } < 1 \Rightarrow$$ Ellipse 
E) ​   $$e = \frac { 1 } { 2 } < 1 \Rightarrow$$ Ellipse 
A) ​   $$e = \frac { 1 } { 2 } < 1 \Rightarrow$$ Ellipse 
B) ​   $$e = \frac { 1 } { 2 } < 1 \Rightarrow$$ Ellipse 
C) ​   $$e = \frac { 1 } { 2 } < 1 \Rightarrow$$ Ellipse 
D) ​   $$e = \frac { 1 } { 2 } < 1 \Rightarrow$$ Ellipse 
E) ​   $$e = \frac { 1 } { 2 } < 1 \Rightarrow$$ Ellipse

Question 4

Find the polar equation of the planet's orbit and the perihelion and aphelion distances. ​
Earth $$a = 95.956 \times 10 ^ { 6 }$$ miles $e = 0.0167$ ​

Accepted Answer

A)  $\frac { 0.9593 \times 10 ^ { 8 } } { 1 - 0.0167 \cos \theta }$ Perihelion distance: $r = 9.4354 \times 10 ^ { 8 }$
Aphelion distance: $r = 9.7558 \times 10 ^ { 8 }$ 
B)  $\frac { 0.9593 \times 10 ^ { 8 } } { 1 - 0.0167 \sin \theta }$ Perihelion distance: $r = 9.7558 \times 10 ^ { 8 }$
Aphelion distance: $r = 9.4354 \times 10 ^ { 8 }$ 
C)  $\frac { 0.0167 \times 10 ^ { 8 } } { 1 + 0.9593 \sin \theta }$ Perihelion distance: $r = 9.4354 \times 10 ^ { 8 }$
Aphelion distance: $r = 9.7558 \times 10 ^ { 8 }$ 
D)  $\frac { 0.9593 \times 10 ^ { 7 } } { 1 - 0.0167 \cos \theta }$ Perihelion distance: $r = 9.7558 \times 10 ^ { 8 }$
Aphelion distance: $r = 9.4354 \times 10 ^ { 8 }$ 
E)  $\frac { 0.9593 \times 10 ^ { 7 } } { 1 + 0.0167 \cos \theta }$ Perihelion distance: $r = 9.4354 \times 10 ^ { 7 }$
Aphelion distance: $r = 9.7558 \times 10 ^ { 7 }$ 
A)  $\frac { 0.9593 \times 10 ^ { 8 } } { 1 - 0.0167 \cos \theta }$ Perihelion distance: $r = 9.4354 \times 10 ^ { 8 }$
Aphelion distance: $r = 9.7558 \times 10 ^ { 8 }$ 
B)  $\frac { 0.9593 \times 10 ^ { 8 } } { 1 - 0.0167 \sin \theta }$ Perihelion distance: $r = 9.7558 \times 10 ^ { 8 }$
Aphelion distance: $r = 9.4354 \times 10 ^ { 8 }$ 
C)  $\frac { 0.0167 \times 10 ^ { 8 } } { 1 + 0.9593 \sin \theta }$ Perihelion distance: $r = 9.4354 \times 10 ^ { 8 }$
Aphelion distance: $r = 9.7558 \times 10 ^ { 8 }$ 
D)  $\frac { 0.9593 \times 10 ^ { 7 } } { 1 - 0.0167 \cos \theta }$ Perihelion distance: $r = 9.7558 \times 10 ^ { 8 }$
Aphelion distance: $r = 9.4354 \times 10 ^ { 8 }$ 
E)  $\frac { 0.9593 \times 10 ^ { 7 } } { 1 + 0.0167 \cos \theta }$ Perihelion distance: $r = 9.4354 \times 10 ^ { 7 }$
Aphelion distance: $r = 9.7558 \times 10 ^ { 7 }$

Question 5

Identify the conic and select its correct graph.​ $$r = \frac { 2.9 } { 2.9 - \cos \theta }$$ ​

Accepted Answer

A)  $$e = \frac { 1 } { 2.9 } < 1 \Rightarrow$$ Ellipse ​  
​
​ 
B)  $$e = \frac { 1 } { 2.9 } < 1 \Rightarrow$$ Ellipse ​  
​ 
C)  $$e = \frac { 1 } { 2.9 } < 1 \Rightarrow$$ Ellipse ​  
​ 
D)  $$e = \frac { 1 } { 2.9 } < 1 \Rightarrow$$ Ellipse ​  
​ 
E)  $$e = \frac { 1 } { 2.9 } < 1 \Rightarrow$$ Ellipse ​  
​ 
A)  $$e = \frac { 1 } { 2.9 } < 1 \Rightarrow$$ Ellipse ​  
​
​ 
B)  $$e = \frac { 1 } { 2.9 } < 1 \Rightarrow$$ Ellipse ​  
​ 
C)  $$e = \frac { 1 } { 2.9 } < 1 \Rightarrow$$ Ellipse ​  
​ 
D)  $$e = \frac { 1 } { 2.9 } < 1 \Rightarrow$$ Ellipse ​  
​ 
E)  $$e = \frac { 1 } { 2.9 } < 1 \Rightarrow$$ Ellipse ​  
​

Question 6

Find a polar equation of the conic with its focus at the pole. ​
Conics
Eccentricity
Directrix
Ellipse $e = \frac { 1 } { 2 }$ $y = 3$ ​
​
​

Accepted Answer

A)  $r = \frac { 3 } { 2 + \sin \theta }$ 
B)  $r = \frac { 3 } { 2 - 4 \sin \theta }$ 
C)  $r = \frac { 4 } { 2 - \sin \theta }$ 
D)  $r = \frac { - 3 } { 2 - \sin \theta }$ 
E)  $r = \frac { 3 } { 2 - \sin \theta }$ 
A)  $r = \frac { 3 } { 2 + \sin \theta }$ 
B)  $r = \frac { 3 } { 2 - 4 \sin \theta }$ 
C)  $r = \frac { 4 } { 2 - \sin \theta }$ 
D)  $r = \frac { - 3 } { 2 - \sin \theta }$ 
E)  $r = \frac { 3 } { 2 - \sin \theta }$

Question 7

Select correct graph to graph rotated conic.​ $$r = \frac { 4 } { 2 + \sin ( \theta + \pi / 6 ) }$$ ​

Accepted Answer

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

Question 8

Identify the conic and select its correct graph.​ $$r = \frac { 3 } { 2 + 6 \sin \theta }$$ ​

Accepted Answer

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

Question 9

The Halley's Comet has an elliptical orbit with an eccentricity of $e \approx 0.967$ .The length of the major axis of the orbit is approximately 35.1 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun? ​

Accepted Answer

A)  $\frac { 1.139 } { 1 - \cos \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
B)  $\frac { 1.139 } { 1 + 0.967 \sin \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
C)  $\frac { 1.139 } { 1 + 1.967 \cos \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
D)  $\frac { 1.139 } { 1 - 1.967 \sin \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
E)  $\frac{0.967}{ 1 + 1.139 \sin \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
A)  $\frac { 1.139 } { 1 - \cos \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
B)  $\frac { 1.139 } { 1 + 0.967 \sin \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
C)  $\frac { 1.139 } { 1 + 1.967 \cos \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
D)  $\frac { 1.139 } { 1 - 1.967 \sin \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
E)  $\frac{0.967}{ 1 + 1.139 \sin \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit.

Question 10

Identify the conic and select its correct graph.​ $$r = \frac { 9 } { 1 + \cos \theta }$$ ​

Accepted Answer

A)  $$e = 1 \Rightarrow$$ Parabola ​   
B)  $$e = 1 \Rightarrow$$ Parabola ​  
​
​ 
C)  $$e = 2 \Rightarrow$$ Hyperbola ​   
D)  $$e = 1 \Rightarrow$$ Parabola ​  
​ 
E)  $$e = 1 \Rightarrow$$ Parabola ​   
A)  $$e = 1 \Rightarrow$$ Parabola ​   
B)  $$e = 1 \Rightarrow$$ Parabola ​  
​
​ 
C)  $$e = 2 \Rightarrow$$ Hyperbola ​   
D)  $$e = 1 \Rightarrow$$ Parabola ​  
​ 
E)  $$e = 1 \Rightarrow$$ Parabola ​

Question 11

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

Question 12

By using a graphing utility select the correct graph of the polar equation.Identify the graph.​ $$\frac { - 3 } { 2 + 8 \sin \theta }$$ ​

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 13

Find a polar equation of the conic with its focus at the pole. ​
Conics
Vertex or vertices
Parabola $$( 1 , - \pi / 2 )$$ ​

Accepted Answer

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

Question 14

Select correct graph to graph rotated conic.​ $$r = \frac { 6 } { 1 - \cos ( \theta - \pi / 4 ) }$$ ​

Accepted Answer

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

Question 15

Select the polar equation with graph.​   ​

Accepted Answer

A)  $\frac { 3 } { 1 - 2 \sin \theta }$ 
B)  $$\frac { 1 } { 1 - 2 \sin \theta }$$ 
C)  $\frac { 3 } { 1 + 2 \cos \theta }$ 
D)  $$\frac { 3 } { 1 + 2 \sin \theta }$$ 
E)  $\frac { 3 } { 1 - 2 \cos \theta }$ 
A)  $\frac { 3 } { 1 - 2 \sin \theta }$ 
B)  $$\frac { 1 } { 1 - 2 \sin \theta }$$ 
C)  $\frac { 3 } { 1 + 2 \cos \theta }$ 
D)  $$\frac { 3 } { 1 + 2 \sin \theta }$$ 
E)  $\frac { 3 } { 1 - 2 \cos \theta }$

Question 16

Identify the conic and select its correct graph.​ $$r = \frac { 6 } { 1 - \cos \theta }$$ ​

Accepted Answer

A)  $e = 1 \Rightarrow$ Parabola ​  
​
​ 
B)  $e = 1 \Rightarrow$ Parabola ​   
C)  $$e = 2 \Rightarrow$$ Hyperbola ​   
D)  $$e = 1 \Rightarrow$$ Parabola ​   
E)  $$e = 1 \Rightarrow$$ Parabola ​  
​ 
A)  $e = 1 \Rightarrow$ Parabola ​  
​
​ 
B)  $e = 1 \Rightarrow$ Parabola ​   
C)  $$e = 2 \Rightarrow$$ Hyperbola ​   
D)  $$e = 1 \Rightarrow$$ Parabola ​   
E)  $$e = 1 \Rightarrow$$ Parabola ​  
​

Question 17

The Roman Coliseum is an elliptical amphitheater measuring approximately 188 meters long and 156 meters wide.Find an equation to model the coliseum that is of the form​ $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ . ​

Accepted Answer

A)  $\frac { x ^ { 2 } } { 6084 } - \frac { y ^ { 2 } } { 8836 } = 1$ 
B)  $\frac { x ^ { 2 } } { 8836 } + \frac { y ^ { 2 } } { 6084 } = 1$ 
C)  $\frac { x ^ { 2 } } { 8836 } + \frac { y ^ { 2 } } { 6084 } = 0$ 
D)  $\frac { x ^ { 2 } } { 188 ^ { 2 } } + \frac { y ^ { 2 } } { 156 ^ { 2 } } = 1$ 
E)  $\frac { x ^ { 2 } } { 6084 } + \frac { y ^ { 2 } } { 8836 } = 0$ 
A)  $\frac { x ^ { 2 } } { 6084 } - \frac { y ^ { 2 } } { 8836 } = 1$ 
B)  $\frac { x ^ { 2 } } { 8836 } + \frac { y ^ { 2 } } { 6084 } = 1$ 
C)  $\frac { x ^ { 2 } } { 8836 } + \frac { y ^ { 2 } } { 6084 } = 0$ 
D)  $\frac { x ^ { 2 } } { 188 ^ { 2 } } + \frac { y ^ { 2 } } { 156 ^ { 2 } } = 1$ 
E)  $\frac { x ^ { 2 } } { 6084 } + \frac { y ^ { 2 } } { 8836 } = 0$

Question 18

Identify the conic and select its correct graph.​ $$r = \frac { 5 } { 5 + \sin \theta }$$ ​

Accepted Answer

A)  $$e = \frac { 1 } { 5 } < 1 \Rightarrow$$ Ellipse ​  
​
​ 
B)  $$e = \frac { 1 } { 5 } < 1 \Rightarrow$$ Ellipse ​   
C)  $$e = \frac { 1 } { 5 } < 1 \Rightarrow$$ Ellipse ​   
D)  $$e = \frac { 1 } { 5 } < 1 \Rightarrow$$ Ellipse ​  
​ 
E)  $$e = \frac { 1 } { 5 } < 1 \Rightarrow$$ Ellipse ​   
A)  $$e = \frac { 1 } { 5 } < 1 \Rightarrow$$ Ellipse ​  
​
​ 
B)  $$e = \frac { 1 } { 5 } < 1 \Rightarrow$$ Ellipse ​   
C)  $$e = \frac { 1 } { 5 } < 1 \Rightarrow$$ Ellipse ​   
D)  $$e = \frac { 1 } { 5 } < 1 \Rightarrow$$ Ellipse ​  
​ 
E)  $$e = \frac { 1 } { 5 } < 1 \Rightarrow$$ Ellipse ​

Question 19

The Comet Borrelly has an elliptical orbit with an eccentricity of ​ $e \approx 0.624$ .The length of the major axis of the orbit is approximately 5.83 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun? ​

Accepted Answer

A)  $\frac { 1.780 } { 1 - 1.624 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
B)  $\frac { 1.780 } { 1 + \cos \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
C)  $\frac { 0.624 } { 1 + 1.780 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
D)  $\frac { 1.780 } { 1 + 0.624 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
E)  $\frac {1.780}{ 1 - 1.624 \cos \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
A)  $\frac { 1.780 } { 1 - 1.624 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
B)  $\frac { 1.780 } { 1 + \cos \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
C)  $\frac { 0.624 } { 1 + 1.780 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
D)  $\frac { 1.780 } { 1 + 0.624 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
E)  $\frac {1.780}{ 1 - 1.624 \cos \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit.

Question 20

Identify the conic and select its correct graph.​ $$r = \frac { 8 } { 1 + \sin \theta }$$ ​

Accepted Answer

A)  $$e = 1 \Rightarrow$$ Parabola ​   
B)  $$e = 1 \Rightarrow$$ Parabola ​   
C)  $$e = 2 \Rightarrow$$ Hyperbola ​  
​ 
D)  $$e = 1 \Rightarrow$$ Parabola ​  
​ 
E)  $$e = 1 \Rightarrow$$ Parabola ​  
​
​ 
A)  $$e = 1 \Rightarrow$$ Parabola ​   
B)  $$e = 1 \Rightarrow$$ Parabola ​   
C)  $$e = 2 \Rightarrow$$ Hyperbola ​  
​ 
D)  $$e = 1 \Rightarrow$$ Parabola ​  
​ 
E)  $$e = 1 \Rightarrow$$ Parabola ​  
​
​

Exam 66: Polar Equations of Conics

Select the polar equation of the conic for ​e = 1.0 and identify the conic for the following equation.​ r=2e1+ecos⁡θr = \frac { 2 e } { 1 + e \cos \theta }r=1+ecosθ2e​ ​

Find a polar equation of the conic with its focus at the pole. ​ Conics Eccentricity Directrix Hyperbola e=65e = \frac { 6 } { 5 }e=56​ x=−3x = - 3x=−3 ​

By using a graphing utility select the correct graph of the polar equation.Identify the graph.​ 122−cos⁡θ\frac { 12 } { 2 - \cos \theta }2−cosθ12​ ​

Find the polar equation of the planet's orbit and the perihelion and aphelion distances. ​ Earth a=95.956×106a = 95.956 \times 10 ^ { 6 }a=95.956×106 miles e=0.0167e = 0.0167e=0.0167 ​

Identify the conic and select its correct graph.​ r=2.92.9−cos⁡θr = \frac { 2.9 } { 2.9 - \cos \theta }r=2.9−cosθ2.9​ ​

Find a polar equation of the conic with its focus at the pole. ​ Conics Eccentricity Directrix Ellipse e=12e = \frac { 1 } { 2 }e=21​ y=3y = 3y=3 ​ ​ ​

Select correct graph to graph rotated conic.​ r=42+sin⁡(θ+π/6)r = \frac { 4 } { 2 + \sin ( \theta + \pi / 6 ) }r=2+sin(θ+π/6)4​ ​

Identify the conic and select its correct graph.​ r=32+6sin⁡θr = \frac { 3 } { 2 + 6 \sin \theta }r=2+6sinθ3​ ​

The Halley's Comet has an elliptical orbit with an eccentricity of e≈0.967e \approx 0.967e≈0.967 .The length of the major axis of the orbit is approximately 35.1 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun? ​

Identify the conic and select its correct graph.​ r=91+cos⁡θr = \frac { 9 } { 1 + \cos \theta }r=1+cosθ9​ ​

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​ ​

By using a graphing utility select the correct graph of the polar equation.Identify the graph.​ −32+8sin⁡θ\frac { - 3 } { 2 + 8 \sin \theta }2+8sinθ−3​ ​

Find a polar equation of the conic with its focus at the pole. ​ Conics Vertex or vertices Parabola (1,−π/2)( 1 , - \pi / 2 )(1,−π/2) ​

Select correct graph to graph rotated conic.​ r=61−cos⁡(θ−π/4)r = \frac { 6 } { 1 - \cos ( \theta - \pi / 4 ) }r=1−cos(θ−π/4)6​ ​

Select the polar equation with graph.​ ​

Identify the conic and select its correct graph.​ r=61−cos⁡θr = \frac { 6 } { 1 - \cos \theta }r=1−cosθ6​ ​

The Roman Coliseum is an elliptical amphitheater measuring approximately 188 meters long and 156 meters wide.Find an equation to model the coliseum that is of the form​ x2a2+y2b2=1\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1a2x2​+b2y2​=1 . ​

Identify the conic and select its correct graph.​ r=55+sin⁡θr = \frac { 5 } { 5 + \sin \theta }r=5+sinθ5​ ​

The Comet Borrelly has an elliptical orbit with an eccentricity of ​ e≈0.624e \approx 0.624e≈0.624 .The length of the major axis of the orbit is approximately 5.83 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun? ​

Identify the conic and select its correct graph.​ r=81+sin⁡θr = \frac { 8 } { 1 + \sin \theta }r=1+sinθ8​ ​

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Sum and Difference Formulas

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Lines

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

Find a polar equation of the conic with its focus at the pole. Conics Eccentricity Directrix Hyperbola $e = \frac { 6 } { 5 }$ $x = - 3$

By using a graphing utility select the correct graph of the polar equation.Identify the graph. $\frac { 12 } { 2 - \cos \theta }$

Find the polar equation of the planet's orbit and the perihelion and aphelion distances. Earth $a = 95.956 \times 10 ^ { 6 }$ miles $e = 0.0167$

Identify the conic and select its correct graph. $r = \frac { 2.9 } { 2.9 - \cos \theta }$

Find a polar equation of the conic with its focus at the pole. Conics Eccentricity Directrix Ellipse $e = \frac { 1 } { 2 }$ $y = 3$

Select correct graph to graph rotated conic. $r = \frac { 4 } { 2 + \sin ( \theta + \pi / 6 ) }$

Identify the conic and select its correct graph. $r = \frac { 3 } { 2 + 6 \sin \theta }$

The Halley's Comet has an elliptical orbit with an eccentricity of $e \approx 0.967$ .The length of the major axis of the orbit is approximately 35.1 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun?

Identify the conic and select its correct graph. $r = \frac { 9 } { 1 + \cos \theta }$

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

By using a graphing utility select the correct graph of the polar equation.Identify the graph. $\frac { - 3 } { 2 + 8 \sin \theta }$

Find a polar equation of the conic with its focus at the pole. Conics Vertex or vertices Parabola $( 1 , - \pi / 2 )$

Select correct graph to graph rotated conic. $r = \frac { 6 } { 1 - \cos ( \theta - \pi / 4 ) }$

Select the polar equation with graph.

Identify the conic and select its correct graph. $r = \frac { 6 } { 1 - \cos \theta }$

The Roman Coliseum is an elliptical amphitheater measuring approximately 188 meters long and 156 meters wide.Find an equation to model the coliseum that is of the form $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ .

Identify the conic and select its correct graph. $r = \frac { 5 } { 5 + \sin \theta }$

The Comet Borrelly has an elliptical orbit with an eccentricity of $e \approx 0.624$ .The length of the major axis of the orbit is approximately 5.83 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun?

Identify the conic and select its correct graph. $r = \frac { 8 } { 1 + \sin \theta }$