Deck 10: Parametric and Polar Curves; Conic Sections

Question 1

Identify the conic section represented by .

A) parabola
B) hyperbola
C) ellipse
D) circle
E) not a conic section

Answer 1

circle

Question 2

Find the distance between the pole and the vertices for the conic that has its focus at the pole and its directrix is units to the right of the pole and its eccentricity is .

A) 4
B) 0.08
C) 0
D) 1
E) 0.32

Answer 2

4

Question 3

Identify the conic section represented by .

A) parabola
B) hyperbola
C) ellipse
D) circle
E) not a conic section

Answer 3

ellipse

Question 4

Identify the conic section represented by .

A) parabola
B) hyperbola
C) ellipse
D) circle
E) not a conic section

Question 5

Find the eccentricity of the conic described by .

A)
B)
C)
D)
E)

Question 6

Find the polar equation for the conic that has its focus at the pole and its directrix is units to the right of the pole and its eccentricity is .

A)
B)
C)
D)
E)

Question 7

Find the polar equation for the conic that has its focus at the pole and its directrix is units to the left of the pole and its eccentricity is .

A)
B)
C)
D)
E)

Question 8

Find the distance between the pole and the vertices for the conic that has its focus at the pole and its directrix is units to the left of the pole and its eccentricity is .

A) 4
B) 0.1
C) 0
D) 1
E) 0.4

Question 9

Find the polar equation for the ellipse that has one of its foci at the pole , eccentricity of , a = 6, and the directrix above the pole.

Question 10

Find the distance from the pole to the vertex of the conic described.

Question 11

Find the eccentricity of the conic described by .

Question 12

Identify the type of conic section by transforming to rectangular coordinates.

Question 13

The directrix of the conic described by is

A) To the right of the pole
B) To the left of the pole
C) Above the pole
D) Below the pole

Question 14

The directrix of the conic described by is how many units to the right of the pole?

A)
B)
C)
D)
E)

Question 15

Identify the conic section represented by .

A) parabola
B) hyperbola
C) ellipse
D) circle
E) not a conic section

Question 16

Find the distance between the pole and the vertices for the conic that has its focus at the pole and its directrix is units above the pole and its eccentricity is .

A) 4
B) 0.04
C) 0
D) 1
E) 0.16

Question 17

Find the polar equation for the conic that has its focus at the pole and its directrix is units below the pole and its eccentricity is .

A)
B)
C)
D)
E)

Question 18

Identify the conic section represented by .

A) parabola
B) hyperbola
C) ellipse
D) circle
E) not a conic section

Question 19

Find the polar equation for the conic that has its focus at the pole and its directrix is units above the pole and its eccentricity is .

A)
B)
C)
D)
E)

Question 20

Find the distance from the pole to the vertex of the conic described.

Question 21

Convert the following equation to polar coordinates.

Question 22

Rotate the coordinates to remove the xy-term. Then, name the conic.

A) circle
B) hyperbola
C) ellipse
D) parabola

Question 23

Identify the type of conic section by transforming to rectangular coordinates.

Question 24

Determine the shape of the curve by eliminating the parameter F $\theta$ and label the direction of increasing $\theta$ .

Question 25

Rotate the coordinates to remove the xy-term. Then, name the conic.

A) circle
B) hyperbola
C) ellipse
D) parabola

Question 26

Rotate the coordinates to remove the xy-term. Then, name the conic.

A) circle
B) hyperbola
C) ellipse
D) parabola

Question 27

Identify the conic section by transforming to rectangular coordinates.

Question 28

Identify the shape of the curve by eliminating the parameter $\theta$ and label the direction of increasing $\theta$ .

Question 29

Identify the conic section by transforming to rectangular coordinates.

Question 30

Rotate the coordinates to remove the xy-term. Then, name the conic.

A) circle
B) hyperbola
C) ellipse
D) parabola

Question 31

Sketch and identify the curve for by eliminating the parameter t and label the direction of increasing t.

Question 32

Rotate the coordinates to remove the xy-term. Then, name the conic.

A) circle
B) hyperbola
C) ellipse
D) parabola

Question 33

Identify the type of conic section by transforming to rectangular coordinates.

Question 34

Rotate the coordinates to remove the xy-term. Then, name the conic.

A) circle
B) hyperbola
C) ellipse
D) parabola

Question 35

Convert the following equation to polar coordinates.

Question 36

Rotate the coordinates to remove the xy-term. Then, name the conic.

A) circle
B) hyperbola
C) ellipse
D) parabola

Question 37

Convert the following equation to polar coordinates.

Question 38

Determine the rotation angle that will eliminate the xy-term.

A)
B)
C)
D)
E)

Question 39

Rotate the coordinates to remove the xy-term. Then, name the conic.

A) circle
B) hyperbola
C) ellipse
D) parabola

Question 40

Rotate the coordinates to remove the xy-term. Then, name the conic.

A) circle
B) hyperbola
C) ellipse
D) parabola

Question 41

Find the center of the ellipse in the x'y'-coordinate system.

Question 42

Find the ends of the major axis of the ellipse in the x'y'-coordinate system.

Question 43

Find the foci of the ellipse in the x'y'-coordinate system.

Question 44

Determine the rotation angle that will eliminate the xy-term.

Question 45

Find the foci of .

Question 46

Rotate the coordinate axes to remove the xy-term. What is the equation in the new coordinate system? What type of conic section is it?

Question 47

Determine the rotation angle that will eliminate the xy-term.

Question 48

Find the vertex of the parabola in the x'y'-coordinate system.

Question 49

Rotate the coordinate axes to remove the xy-term. What is the equation in the new coordinate system? What type of conic section is it?

Question 50

The vertex of the parabola is

A) (2, 0)
B) (0, 2)
C) (0, 0)
D) (1, 2)
E) (2, 2)

Question 51

Find the center of the hyperbola in the xy-coordinate system.

Question 52

Rotate the coordinate axes to remove the xy-term. What is the equation in the new coordinate system? What type of conic section is it?

Question 53

Find the ends of the minor axis of the ellipse in the x'y'-coordinate system.

Question 54

Find the vertex of the parabola in the x'y'-coordinate system.

Question 55

Find the ends of the minor axis of the ellipse in the x'y'-coordinate system.

Question 56

Determine the rotation angle that will eliminate the xy-term.

A)
B)
C)
D)
E)

Question 57

Determine the rotation angle that will eliminate the xy-term.

Question 58

Find the ends of the major axis of the ellipse in the x'y'-coordinate system.

Question 59

Find the asymptotes of .

Question 60

Find the vertices of the hyperbola in the xy-coordinate system.

Question 61

Find the equation of the hyperbola with vertices and asymptotes .

A)
B)
C)
D)
E)

Question 62

Find the equation of the hyperbola with foci and vertices units apart.

A)
B)
C)
D)
E)

Question 63

Find the equation of the hyperbola with foci and vertices units apart.

A)
B)
C)
D)
E)

Question 64

Find the equation of the ellipse with a major axis length of , a minor axis length of , center at (0, 0), and foci on the x-axis.

A)
B)
C)
D)
E)

Question 65

Sketch the parabola 2x²- 10x + 5y + 12 = 0 showing the focus, vertex and directrix.

Question 66

Find the equation of the hyperbola with foci and vertices units apart.

A)
B)
C)
D)
E)

Question 67

State the definition of a parabola. Use your definition to derive the equation of the parabola whose focus is at F(3, 9) and directrix x = 1.

Question 68

Find the equation of the ellipse with foci and such that the distances from the foci to any point on the ellipse sum to 34.

A)
B)
C)
D)
E)

Question 69

Sketch the parabola y² + 6y + 6x = 0 showing the focus, vertex and directrix.

Question 70

Find the equation of the hyperbola with foci and vertices units apart.

A)
B)
C)
D)
E)

Question 71

Sketch the parabola 9y² = 24x - 48 showing the focus, vertex and directrix.

Question 72

Find the equation of the parabola with vertex ( , 3) and directrix

A)
B)
C)
D)
E)

Question 73

Find the equation of the ellipse with a major axis length of , a minor axis length of , center at , and foci on .

A)
B)
C)
D)
E)

Question 74

Find the equation for the parabola whose directrix is x = 6 and vertex at (9, 6). Where is the focus located?

Question 75

Sketch the parabola y² - 4y- 7x + 11 = 0 showing the focus, vertex, and directrix.

Question 76

Find the equation of the hyperbola with vertices and asymptotes .

A)
B)
C)
D)
E)

Question 77

Find the equation of the ellipse with a major axis length of , a minor axis length of , center at (0, 0), and foci on the y-axis.

A)
B)
C)
D)
E)

Question 78

Find the equation of the parabola with focus at (6, -1) and directrix x = 2. Sketch.

Question 79

Sketch the parabola x²- 10x - 2y 13 = 0 showing the focus, vertex and directrix.

Question 80

Find the equation of the ellipse with a major axis length of , a minor axis length of , center at , and foci on .

A)
B)
C)
D)
E)