Deck 6: Topics-In-Analytic-Geometry

Question 1

Identify the conic and select its correct graph. ​ ​

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

Answer 1

Hyperbola ​
​

Question 2

Find a polar equation of the conic with its focus at the pole. ​
Conics
Eccentricity
Directrix
Ellipse ​
​
​

A)
B)
C)
D)
E)

Answer 2

Question 3

Identify the conic and select its correct graph. ​ ​

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

Answer 3

Ellipse ​
​

Question 4

Select the polar equation of the conic for ​e = 1.0 and identify the conic for the following equation. ​ ​

A)
B)
C)
D)
E)

Question 5

Identify the conic and select its correct graph. ​ ​

A) Parabola ​
B) Parabola ​
​
​
C) Hyperbola ​
D) Parabola ​
​
E) Parabola ​

Question 6

Select the polar equation of the conic for ​e = 0.75 and identify the conic for the following equation. ​ ​

A)
B)
C)
D)
E)

Question 7

Find a polar equation of the conic with its focus at the pole. ​
Conics
Eccentrity
Directrix
Parabola ​
​

A)
B)
C)​
D)
E)

Question 8

Find a polar equation of the conic with its focus at the pole. ​
Conics
​Eccentrity
Directrix
Hyperbola ​

A)
B)
C)
D)
E)

Question 9

Identify the conic and select its correct graph. ​ ​

A) Parabola ​
​
​
B) Parabola ​
C) Hyperbola ​
D) Parabola ​
E) Parabola ​
​

Question 10

Find a polar equation of the conic with its focus at the pole. ​
Conics
Eccentrity
Directrix
Ellipse ​​

A)
B)
C)
D)
E)

Question 11

Select the polar equation of the conic for ​e = 1.0 and identify the conic for the following equation. ​ ​

A)
B)
C)
D)
E)

Question 12

Identify the conic and select its correct graph. ​ ​

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

Question 13

Identify the conic and select its correct graph. ​ ​

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

Question 14

Identify the conic and select its correct graph. ​ ​

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

Question 15

Find a polar equation of the conic with its focus at the pole. ​
Conics
Eccentricity
Directrix
Hyperbola ​

A)
B)
C)
D)
E)

Question 16

Identify the conic and select its correct graph. ​ ​

A) Hyperbola ​
B) Parabola ​
​
C) Parabola ​
D) Parabola ​
E) Parabola ​
​
​

Question 17

Select the polar equation of the conic for ​e = 1.0 and identify the conic for the following equation. ​ ​

A)
B)
C)
D)
E)

Question 18

Identify the conic and select its correct graph. ​ ​

A) Parabola ​
B) Parabola ​
C) Hyperbola ​
​
D) Parabola ​
​
E) Parabola ​
​
​

Question 19

Identify the conic and select its correct graph. ​ ​

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

Question 20

Find a polar equation of the conic with its focus at the pole. ​
Conics
Eccentrity
Directrix
Parabola ​
​

A) ​
B)
C)
D) ​
E)

Question 21

Identify the conic and select its correct graph. ​ ​

A) Hyperbola ​
​
​
B) Ellipse ​
C) Hyperbola ​
D) Ellipse ​
​
E) Hyperbola ​

Question 22

Select correct graph to graph rotated conic. ​ ​

A)​
B)​
C)​
D)​
E)​

Question 23

Select the polar equation of graph. ​ ​

A)
B)
C)
D) ​
E)

Question 24

By using a graphing utility select the correct graph of the polar equation. ​ ​

A)​ ​
B)​
C)​
D)​
E)​

Question 25

Select the polar equation with graph. ​ ​

A)
B)
C)
D)
E)

Question 26

Select the polar equation of graph. ​ ​

A)
B)
C)
D)
E)

Question 27

Find a polar equation of the conic with its focus at the pole. ​
Conics
Vertex or vertices
Parabola ​

A)
B)
C)
D)
E)

Question 28

By using a graphing utility select the correct graph of the polar equation.Identify the graph. ​ ​

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

Question 29

Select the polar equation with graph. ​ ​

A)
B)
C)
D)
E)

Question 30

Select the polar equation of graph. ​ ​

A)
B)
C)
D)
E)

Question 31

Identify the conic and select its correct graph. ​ ​

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

Question 32

Select correct graph to graph rotated conic. ​ ​

A)​
B)​
C)​
D)​
E)​

Question 33

Find a polar equation of the conic with its focus at the pole. ​
Conics
Vertex or vertices
Parabola ​

A)
B)
C)
D)
E)

Question 34

Select correct graph to graph rotated conic. ​ ​

A)​
B)​
C)​
D)​
E)​

Question 35

Select correct graph to graph rotated conic. ​ ​

A)​
B)​
C)​ ​
D)​
E)​

Question 36

Find a polar equation of the conic with its focus at the pole. ​
Conics
Vertex or vertices
Parabola ​

A)
B)
C)
D)
E)

Question 37

Find a polar equation of the conic with its focus at the pole. ​
Conics
Vertex or vertices
Parabola ​

A)
B)
C)
D)
E)

Question 38

By using a graphing utility select the correct graph of the polar equation.Identify the graph. ​ ​

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

Question 39

Identify the conic and select its correct graph. ​ ​

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

Question 40

Select the polar equation of graph. ​ ​

A)
B)
C)
D)
E)

Question 41

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to , polar axis, pole Circle with radius
​
B)Symmetric with respect to , polar axis, pole Circle with radius
​
C)Symmetric with respect to , polar axis, pole Circle with radius
​
D)Symmetric with respect to , polar axis, pole Circle with radius
​
E)Symmetric with respect to , polar axis, pole Circle with radius
​

Question 42

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to polar axis ​
B)Symmetric with respect to polar axis ​
​
C)Symmetric with respect to polar axis ​
D)Symmetric with respect to polar axis ​
E)Symmetric with respect to polar axis ​

Question 43

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to , polar axis, pole Circle with radius
​
B)Symmetric with respect to , polar axis, pole Circle with radius
​
C)Symmetric with respect to , polar axis, pole Circle with radius
​
D)Symmetric with respect to , polar axis, pole Circle with radius
​
E)Symmetric with respect to , polar axis, pole Circle with radius
​

Question 44

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to , polar axis, pole Circle with radius
​
B)Symmetric with respect to , polar axis, pole Circle with radius
​
C)Symmetric with respect to , polar axis, pole Circle with radius
​
D)Symmetric with respect to , polar axis, pole Circle with radius
​
E)Symmetric with respect to , polar axis, pole Circle with radius
​

Question 45

By using a graphing utility select the correct graph of the polar equation.Identify the graph. ​ ​

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

Question 46

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 ​ .
​

A)
B)
C)
D)
E)

Question 47

The Comet Borrelly has an elliptical orbit with an eccentricity of ​ .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? ​

A) Closest point to the sun is 1.096 astronomical unit.
B) Closest point to the sun is 1.096 astronomical unit.
C) Closest point to the sun is 1.096 astronomical unit.
D) Closest point to the sun is 1.096 astronomical unit.
E) Closest point to the sun is 1.096 astronomical unit.

Question 48

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to ​
​
B)Symmetric with respect to ​
C)Symmetric with respect to ​
D)Symmetric with respect to ​
E)Symmetric with respect to ​

Question 49

Consider the polar equation: ​ ​
Identify the conic without graphing the equation.
​

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

Question 50

Find the polar equation of the planet's orbit and the perihelion and aphelion distances. ​
Earth miles ​

A) Perihelion distance:
Aphelion distance:
B) Perihelion distance:
Aphelion distance:
C) Perihelion distance:
Aphelion distance:
D) Perihelion distance:
Aphelion distance:
E) Perihelion distance:
Aphelion distance:

Question 51

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to , polar axis, pole Circle with radius
​
B)Symmetric with respect to , polar axis, pole Circle with radius
​
C)Symmetric with respect to , polar axis, pole Circle with radius
​
D)Symmetric with respect to , polar axis, pole Circle with radius
​
E)Symmetric with respect to , polar axis, pole Circle with radius
​

Question 52

The Halley's Comet has an elliptical orbit with an eccentricity of .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? ​

A) Closest point to the sun is 0.579 astronomical unit.
B) Closest point to the sun is 0.579 astronomical unit.
C) Closest point to the sun is 0.579 astronomical unit.
D) Closest point to the sun is 0.579 astronomical unit.
E) Closest point to the sun is 0.579 astronomical unit.

Question 53

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to ​
B)Symmetric with respect to ​
C)Symmetric with respect to ​
D)Symmetric with respect to ​
E)Symmetric with respect to ​

Question 54

By using a graphing utility select the correct graph of the polar equation.Identify the graph. ​ ​

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

Question 55

Use the following results the polar equation of the ellipse is to write the polar form of the equation of the conic . ​

A)
B)
C)
D)
E)

Question 56

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to ​
B)Symmetric with respect to ​
C)Symmetric with respect to ​
D)Symmetric with respect to ​
E)Symmetric with respect to ​

Question 57

Use the following results the polar equation of the hyperbolla is to write the polar form of the equation of the conic . ​

A)
B)
C)
D)
E)

Question 58

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to polar axis
B)Symmetric with respect to polar axis
C)Symmetric with respect to polar axis
D)Symmetric with respect to polar axis ​
E)Symmetric with respect to polar axis

Question 59

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to polar axis Circle with radius 2.5
​
B)Symmetric with respect to polar axis Circle with radius 2.5
​
C)Symmetric with respect to polar axis Circle with radius 2.5
​
D)Symmetric with respect to polar axis Circle with radius 2.5
​
E)Symmetric with respect to polar axis Circle with radius 2.5
​

Question 60

A satellite in a 100-mile-high circular orbit around Earth has a velocity of approximately 17,500 miles per hour.If this velocity is multiplied by , the satellite will have the minimum velocity necessary to escape Earth's gravity and will follow a parabolic path with the center of Earth as the focus.(Hints: The radius of Earth is 4000 miles.) ​ Find the distance between the surface of the Earth and the satellite when .
​

A)Distance between surface of Earth and satellite:4496 miles
B)Distance between surface of Earth and satellite:4322 miles
C)Distance between surface of Earth and satellite:1286 miles
D)Distance between surface of Earth and satellite:643 miles
E)Distance between surface of Earth and satellite:1492 miles

Question 61

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)
B)
C)
D)
E)

Question 62

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to polar axis ​
B)Symmetric with respect to polar axis ​
C)Symmetric with respect to polar axis ​
D)Symmetric with respect to polar axis ​
E)Symmetric with respect to polar axis ​

Question 63

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to , the polar axis, and the pole ​
B)Symmetric with respect to , the polar axis, and the pole ​
C)Symmetric with respect to , the polar axis, and the pole ​
D)Symmetric with respect to , the polar axis, and the pole ​
E)Symmetric with respect to , the polar axis, and the pole ​

Question 64

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)
B)
C)
D)
E)

Question 65

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to the polar axis ​
B)Symmetric with respect to the polar axis ​
​
C)Symmetric with respect to the polar axis ​
​
​
D)Symmetric with respect to the polar axis ​
​
E)Symmetric with respect to the polar axis ​
​

Question 66

Select the graph of the equation. ​ ​

A)​
B)​
C)​
D)​
E)​

Question 67

Select the graph of over the interval.Describe the part of the graph obtained in this case. ​ ​

A)​ Lower half of circle
B)​ Lower half of circle
C)​ Lower half of circle
D)​ Lower half of circle
E)​ Lower half of circle

Question 68

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to the polar axis ​
B)Symmetric with respect to the polar axis ​
C)Symmetric with respect to the polar axis ​
D)Symmetric with respect to the polar axis ​
E)Symmetric with respect to the polar axis ​

Question 69

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 70

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to the polar axis ​
B)Symmetric with respect to the polar axis ​
C)Symmetric with respect to the polar axis ​
D)Symmetric with respect to the polar axis ​
E)Symmetric with respect to the polar axis ​

Question 71

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 72

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to the polar axis, , and the pole
Lemniscate
​
B)Symmetric with respect to the polar axis, , and the pole
Lemniscate
​
C)Symmetric with respect to the polar axis, , and the pole
Lemniscate
​
D)Symmetric with respect to the polar axis, , and the pole
Lemniscate
​
E)Symmetric with respect to the polar axis, , and the pole
Lemniscate
​

Question 73

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to the polar axis ​
B)Symmetric with respect to the polar axis ​
C)Symmetric with respect to the polar axis ​
D)Symmetric with respect to the polar axis ​
E)Symmetric with respect to the polar axis ​

Question 74

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to ​
B)Symmetric with respect to ​
C)Symmetric with respect to ​
D)Symmetric with respect to ​
E)Symmetric with respect to ​

Question 75

Select the graph of over the interval.Describe the part of the graph obtained in this case. ​ ​

A)​ Entire circle
B)​ Entire circle
C)​ Entire circle
D)​ Entire circle
E)​ Entire circle

Question 76

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 77

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to ​
B)Symmetric with respect to ​
C)Symmetric with respect to ​
D)Symmetric with respect to ​
E)Symmetric with respect to ​

Question 78

Select the graph of over the interval.Describe the part of the graph obtained in this case. ​ ​

A)​ Left half of circle
B)​ Left half of circle
C)​ Left half of circle
D)​ Left half of circle
E)​ Left half of circle

Question 79

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​ ​

A)Symmetric with respect to ​
B)Symmetric with respect to ​
C)Symmetric with respect to ​
D)Symmetric with respect to ​
E)Symmetric with respect to ​

Question 80

Select the graph of over the interval.Describe the part of the graph obtained in this case. ​ ​

A)​ Upper half of circle
B)​ Upper half of circle
C)​ Upper half of circle
D)​ Upper half of circle
E)​ Upper half of circle