Deck 10: Topics in Analytic Geometry

Question 1

Find the center and foci of the ellipse.

A)center: foci:
B)center: foci:
C)center: foci:
D)center: foci:
E)center: foci:

Answer 1

center: foci:

Question 2

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: foci:

A)
B)
C)
D)
E)

Answer 2

Question 3

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (0, -2), (6, -2)
Asymptotes:

A)
B)
C)
D)
E)

Answer 3

Question 4

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, 7)

A)x² = -7y
B)y² = 7x
C)x² = 7y
D)y² = 28x
E)x² = 28y

Question 5

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

A)
B)
C)
D)
E)

Question 6

A solar oven uses a parabolic reflector to focus the sun's rays at a point 8 inches from the vertex of the reflector (see figure). Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin. L = 8 inches

A)
B)
C)
D)
E)

Question 7

Find the standard form of the equation of the ellipse with vertices and eccentricity .

A)
B)
C)
D)
E)

Question 8

Find the center and vertices of the ellipse.

A)center: vertices:
B)center: vertices:
C)center: vertices:
D)center: vertices:
E)center: vertices:

Question 9

Find the vertex and directrix of the parabola.

A)vertex: directrix:
B)vertex: directrix:
C)vertex: directrix:
D)vertex: directrix:
E)vertex: directrix:

Question 10

Find the vertices and asymptotes of the hyperbola.

A)vertices: asymptote:
B)vertices: asymptote:
C)vertices: asymptote:
D)vertices: asymptote:
E)vertices: asymptote:

Question 11

An elliptical stained-glass insert is to be fitted in a rectangular opening (see figure). Using the coordinate system shown, find an equation for the ellipse.

A)
B)
C)
D)
E)

Question 12

Find the vertex and focus of the parabola.

A)vertex: (0, 0) focus:
B)vertex: focus:
C)vertex: focus:
D)vertex: (0, 0) focus:
E)vertex: (0, 0) focus:

Question 13

Find the vertices and asymptotes of the hyperbola.

A)vertices: asymptote:
B)vertices: asymptote:
C)vertices: asymptote:
D)vertices: asymptote:
E)vertices: asymptote:

Question 14

Find the center and vertices of the ellipse.

A)center: (7, 0) vertices: (0, -6), (0, 6)
B)center: (0, 0) vertices: (0, -7), (0, 7)
C)center: (0, 0) vertices: (-6, 0), (6, 0)
D)center: (7, 6) vertices: (-7, -6), (7, 6)
E)center: (0, 0) vertices: (-7, 0), (7, 0)

Question 15

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -1

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

Question 16

Find the standard form of the equation of the ellipse with the following characteristics. foci: major axis of length: 20

A)
B)
C)
D)
E)

Question 17

Find the center and vertices of the ellipse. = 0

A)center: (-3, -7) vertices: (-6, -7), (0, -7)
B)center: (3, 7) vertices: (2, 7), (4, 7)
C)center: (3, 7) vertices: (0, 7), (6, 7)
D)center: (-7, -3) vertices: (-10, -3), (-4, -3)
E)center: (-3, -7) vertices: (-4, -7), (-2, -7)

Question 18

Find the vertex and focus of the parabola.

A)vertex: (0, 0) focus:
B)vertex: focus: (0, 0)
C)vertex: focus: (0, 0)
D)vertex: (0, 0) focus:
E)vertex: (0, 0) focus:

Question 19

Find the center and vertices of the hyperbola.

A)center: (3,-4), vertices: (1, -4), (5, -4)
B)center: (-4, 3), vertices: (-6, 3), (-2, 3)
C)center: (3, -4), vertices: (3, -6), (3, -2)
D)center: (-3, 4), vertices: (-5, 4), (-1,4)
E)center: (-3, 4), vertices: (-3, 2), (-3, 6)

Question 20

Find the standard form of the equation of the hyperbola with the given characteristics. foci: asymptotes:

A)
B)
C)
D)
E)

Question 21

Find the vertices and asymptotes of the hyperbola.

A)vertices: asymptote:
B)vertices: asymptote:
C)vertices: asymptote:
D)vertices: asymptote:
E)vertices: asymptote:

Question 22

An elliptical stained-glass insert is to be fitted in a rectangular opening (see figure). Using the coordinate system shown, find an equation for the ellipse.

A)
B)
C)
D)
E)

Question 23

Identify the conic by writing the equation in standard form.

A) ; ellipse
B) ; ellipse
C) ; ellipse
D) ; ellipse
E) ; circle

Question 24

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -3

A)y² = 12x
B)x² = -3y
C)y² = -3x
D)x² = 12y
E)x² = -12y

Question 25

Find the center and vertices of the ellipse. = 0

A)center: (8, 7) vertices: (6, 7), (10, 7)
B)center: (8, 7) vertices: (7, 7), (9, 7)
C)center: (-8, -7) vertices: (-10, -7), (-6, -7)
D)center: (7, 8) vertices: (5, 8), (9, 8)
E)center: (-8, -7) vertices: (-9, -7), (-7, -7)

Question 26

Find the standard form of the equation of the ellipse with the given characteristics. foci: endpoints of the major axis:

A)
B)
C)
D)
E)

Question 27

Find the center and vertices of the ellipse.

A)center: vertices:
B)center: vertices:
C)center: vertices:
D)center: vertices:
E)center: vertices:

Question 28

Identify the conic by writing the equation in standard form.

A) ; hyperbola
B) ; ellipse
C) ; ellipse
D) ; hyperbola
E) ; hyperbola

Question 29

Find the vertex and focus of the parabola.

A)vertex: focus:
B)vertex: (0, 0) focus:
C)vertex: (0, 0) focus:
D)vertex: (0, 0) focus:
E)vertex: focus:

Question 30

Find the vertices and asymptotes of the hyperbola.

A)vertices: asymptote:
B)vertices: asymptote:
C)vertices: asymptote:
D)vertices: asymptote:
E)vertices: asymptote:

Question 31

Identify the conic by writing the equation in standard form.

A) ; ellipse
B) ; circle
C) ; circle
D) ; ellipse
E) ; circle0

Question 32

Find the center and vertices of the ellipse.

A)center: (0, 0) vertices: (0, -8), (0, 8)
B)center: (8, 7) vertices: (-8, -7), (8, 7)
C)center: (0, 0) vertices: (-8, 0), (8, 0)
D)center: (8, 0) vertices: (0, -7), (0, 7)
E)center: (0, 0) vertices: (-7, 0), (7, 0)

Question 33

Find the standard form of the equation of the ellipse with the given characteristics. foci: endpoints of the major axis:

A)
B)
C)
D)
E)

Question 34

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: foci:

A)
B)
C)
D)
E)

Question 35

Find the center and vertices of the hyperbola.

A)center: (-5, 3), vertices: (-5, 1), (-5, 5)
B)center: (5, -3), vertices: (5, -5), (5, -1)
C)center: (3, -5), vertices: (1, -5), (5, -5)
D)center: (5, -3), vertices: (3, -3), (7,-3)
E)center: (-5,3), vertices: (-7, 3), (-3, 3)

Question 36

Find the vertex and directrix of the parabola.

A)vertex: directrix:
B)vertex: directrix:
C)vertex: directrix:
D)vertex: directrix:
E)vertex: directrix:

Question 37

Find the vertex and focus of the parabola.

A)vertex: focus: (0, 0)
B)vertex: (0, 0) focus:
C)vertex: (0, 0) focus:
D)vertex: focus: (0, 0)
E)vertex: (0, 0) focus:

Question 38

Find the center and foci of the ellipse.

A)center: foci:
B)center: foci:
C)center: foci:
D)center: foci:
E)center: foci:

Question 39

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -6)

A)y² = -6x
B)x² = 6y
C)x² = -24y
D)x² = -6y
E)y² = -24x

Question 40

Find the standard form of the equation of the ellipse with vertices and eccentricity .

A)
B)
C)
D)
E)

Question 41

Find the standard form of the equation of the hyperbola with the given characteristics. foci: asymptotes:

A)
B)
C)
D)
E)

Question 42

Identify the conic by writing the equation in standard form.

A) ; ellipse
B) ; hyperbola
C) ; hyperbola
D) ; ellipse
E) ; hyperbola

Question 43

Find the center and vertices of the ellipse.

A)center: vertices:
B)center: vertices:
C)center: vertices:
D)center: vertices:
E)center: vertices:

Question 44

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

A)
B)
C)
D)
E)

Question 45

An elliptical stained-glass insert is to be fitted in a rectangular opening (see figure). Using the coordinate system shown, find an equation for the ellipse.

A)
B)
C)
D)
E)

Question 46

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (-2, 1), (6, 1)
Asymptotes:

A)
B)
C)
D)
E)

Question 47

Find the standard form of the equation of the ellipse with the given characteristics. foci: endpoints of the major axis:

A)
B)
C)
D)
E)

Question 48

Find the standard form of the equation of the ellipse with the following characteristics. foci: major axis of length: 20

A)
B)
C)
D)
E)

Question 49

Find the vertex and focus of the parabola.

A)vertex: focus: (0, 0)
B)vertex: focus: (0, 0)
C)vertex: (0, 0) focus:
D)vertex: (0, 0) focus:
E)vertex: (0, 0) focus:

Question 50

Find the standard form of the equation of the ellipse with vertices and eccentricity .

A)
B)
C)
D)
E)

Question 51

Find the vertex and focus of the parabola.

A)vertex: focus:
B)vertex: (0, 0) focus:
C)vertex: (0, 0) focus:
D)vertex: (0, 0) focus:
E)vertex: focus:

Question 52

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, 7)

A)x² = 28y
B)x² = 7y
C)x² = -7y
D)y² = 28x
E)y² = 7x

Question 53

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 1

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

Question 54

Find the center and foci of the ellipse.

A)center: foci:
B)center: foci:
C)center: foci:
D)center: foci:
E)center: foci:

Question 55

Identify the conic by writing the equation in standard form.

A) ; ellipse
B) ; circle
C) ; circle
D) ; circle
E) ; ellipse0

Question 56

Find the center and vertices of the ellipse.

A)center: (7, 2) vertices: (-7, -2), (7, 2)
B)center: (0, 0) vertices: (0, -7), (0, 7)
C)center: (7, 0) vertices: (0, -2), (0, 2)
D)center: (0, 0) vertices: (-2, 0), (2, 0)
E)center: (0, 0) vertices: (-7, 0), (7, 0)

Question 57

Identify the conic by writing the equation in standard form.

A) ; circle
B) ; ellipse
C) ; ellipse
D) ; ellipse
E) ; ellipse

Question 58

Find the vertex and directrix of the parabola.

A)vertex: directrix:
B)vertex: directrix:
C)vertex: directrix:
D)vertex: directrix:
E)vertex: directrix:

Question 59

Find the standard form of the equation of the ellipse with the given characteristics. foci: endpoints of the major axis:

A)
B)
C)
D)
E)

Question 60

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure). Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin. L = 5 inches

A)
B)
C)
D)
E)

Question 61

Give the coordinates of the circle's center and its radius.

A)(-4, 8); r = 5
B)(-4, 8); r = 25
C)(4, -8); r = 5
D)(4, -8); r = 25
E)none of these

Question 62

Identify the conic by writing the equation in standard form.

A) ; ellipse
B) ; ellipse
C) ; ellipse
D) ; ellipse
E) ; circle

Question 63

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (0, -1), (10, -1)
Asymptotes:

A)
B)
C)
D)
E)

Question 64

Find the standard form of the equation of the ellipse with the given characteristics. foci: endpoints of the major axis:

A)
B)
C)
D)
E)

Question 65

Graph the following equation.

A)
B)
C)

Question 66

Find the standard form of the equation of the ellipse with the following characteristics. foci: major axis of length: 12

A)
B)
C)
D)
E)

Question 67

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: foci:

A)
B)
C)
D)
E)

Question 68

Give the coordinates of the circle's center and its radius.

A)(1, 1); r = 100
B)(0, 0); r = 100
C)(1, 1); r = 10
D)(0, 0); r = 10
E)none of these

Question 69

A solar oven uses a parabolic reflector to focus the sun's rays at a point 6 inches from the vertex of the reflector (see figure). Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin. L = 6 inches

A)
B)
C)
D)
E)

Question 70

Find the vertices and asymptotes of the hyperbola.

A)vertices: asymptote:
B)vertices: asymptote:
C)vertices: asymptote:
D)vertices: asymptote:
E)vertices: asymptote:

Question 71

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

A)
B)
C)
D)
E)

Question 72

Find the vertices and asymptotes of the hyperbola.

A)vertices: asymptote:
B)vertices: asymptote:
C)vertices: asymptote:
D)vertices: asymptote:
E)vertices: asymptote:

Question 73

Find the standard form of the equation of the hyperbola with the given characteristics. foci: asymptotes:

A)
B)
C)
D)
E)

Question 74

Identify the conic by writing the equation in standard form.

A) ; ellipse
B) ; ellipse
C) ; circle
D) ; circle
E) ; circle0

Question 75

Find the vertex and directrix of the parabola.

A)vertex: directrix:
B)vertex: directrix:
C)vertex: directrix:
D)vertex: directrix:
E)vertex: directrix:

Question 76

Identify the conic by writing the equation in standard form.

A) ; hyperbola
B) ; hyperbola
C) ; hyperbola
D) ; ellipse
E) ; ellipse

Question 77

Find the equation of the circle graphed below.

A)
B)
C)
D)
E)

Question 78

Find the center and vertices of the ellipse. = 0

A)center: (3, -8) vertices: (0, -8), (6, -8)
B)center: (8, -3) vertices: (7, -3), (9, -3)
C)center: (-8, 3) vertices: (-9, 3), (-7, 3)
D)center: (-8, 3) vertices: (-11, 3), (-5, 3)
E)center: (8, -3) vertices: (5, -3), (11, -3)

Question 79

Find the center and vertices of the hyperbola.

A)center: (1, -5), vertices: (1, -10), (1, 0)
B)center: (-1, 5), vertices: (-1, 0), (-1, 10)
C)center: (-1, 5), vertices: (-6, 5), (4,5)
D)center: (1,-5), vertices: (-4, -5), (6, -5)
E)center: (-5, 1), vertices: (-10, 1), (0, 1)

Question 80

Find the standard form of the equation of the ellipse with the given characteristics. foci: endpoints of the major axis:

A)
B)
C)
D)
E)