Deck 10: Topics in Analytic Geometry

Question 1

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

Answer 1

y² = 4x

Question 2

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

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 center and vertices of the ellipse.

A) center: vertices:

B) center: vertices:

C) center: vertices:

D) center: vertices:

E) center: vertices:

Question 5

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 6

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

A)
B)
C)
D)
E)

Question 7

Find the vertex and directrix of the parabola.

A) vertex: directrix:

B) vertex: directrix:

C) vertex: directrix:

D) vertex: directrix:

E) vertex: directrix:

Question 8

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 9

Find the center and foci of the ellipse.

A) center: foci:

B) center: foci:

C) center: foci:

D) center: foci:

E) center: foci:

Question 10

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

A)
B)
C)
D)
E)

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 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 13

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 14

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 15

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

A)
B)
C)
D)
E)

Question 16

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 17

Find the vertices and asymptotes of the hyperbola.

A) vertices: asymptote:

B) vertices: asymptote:

C) vertices: asymptote:

D) vertices: asymptote:

E) vertices: asymptote:

Question 18

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 19

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 20

Find the vertices and asymptotes of the hyperbola.

A) vertices: asymptote:

B) vertices: asymptote:

C) vertices: asymptote:

D) vertices: asymptote:

E) vertices: asymptote:

Question 21

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

A)
B)
C)
D)
E)

Question 22

Find the vertices and asymptotes of the hyperbola.

A) vertices: asymptote:

B) vertices: asymptote:

C) vertices: asymptote:

D) vertices: asymptote:

E) vertices: asymptote:

Question 23

Identify the conic by writing the equation in standard form.

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

Question 24

Identify the conic by writing the equation in standard form.

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

Question 25

Identify the conic by writing the equation in standard form.

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

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 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 28

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

A)
B)
C)
D)
E)

Question 29

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 30

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 31

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 32

Find the vertices and asymptotes of the hyperbola.

A) vertices: asymptote:

B) vertices: asymptote:

C) vertices: asymptote:

D) vertices: asymptote:

E) vertices: asymptote:

Question 33

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 34

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 35

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 36

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 37

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 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 center and vertices of the ellipse.

A) center: vertices:

B) center: vertices:

C) center: vertices:

D) center: vertices:

E) center: vertices:

Question 40

Find the vertex and directrix of the parabola.

A) vertex: directrix:

B) vertex: directrix:

C) vertex: directrix:

D) vertex: directrix:

E) vertex: directrix:

Question 41

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 42

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 43

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

A)
B)
C)
D)
E)

Question 44

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 45

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 46

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 47

Identify the conic by writing the equation in standard form.

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

Question 48

Find the center and vertices of the ellipse.

A) center: vertices:

B) center: vertices:

C) center: vertices:

D) center: vertices:

E) center: vertices:

Question 49

Find the vertex and directrix of the parabola.

A) vertex: directrix:

B) vertex: directrix:

C) vertex: directrix:

D) vertex: directrix:

E) vertex: directrix:

Question 50

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 51

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

A)
B)
C)
D)
E)

Question 52

Identify the conic by writing the equation in standard form.

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

Question 53

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 54

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 55

Identify the conic by writing the equation in standard form.

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

Question 56

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

A)
B)
C)
D)
E)

Question 57

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 58

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 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

Find the center and foci of the ellipse.

A) center: foci:

B) center: foci:

C) center: foci:

D) center: foci:

E) center: foci:

Question 61

Find the vertices and asymptotes of the hyperbola.

A) vertices: asymptote:

B) vertices: asymptote:

C) vertices: asymptote:

D) vertices: asymptote:

E) vertices: asymptote:

Question 62

Find the equation of the circle graphed below.

A)
B)
C)
D)
E)

Question 63

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 64

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

A)
B)
C)
D)
E)

Question 65

Identify the conic by writing the equation in standard form.

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

Question 66

Find the vertices and asymptotes of the hyperbola.

A) vertices: asymptote:

B) vertices: asymptote:

C) vertices: asymptote:

D) vertices: asymptote:

E) vertices: asymptote:

Question 67

Identify the conic by writing the equation in standard form.

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

Question 68

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 69

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 70

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

A)
B)
C)
D)
E)

Question 71

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 72

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 73

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 74

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 75

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

A)
B)
C)
D)
E)

Question 76

Graph the following equation.

A)
B)
C)

Question 77

Find the vertex and directrix of the parabola.

A) vertex: directrix:

B) vertex: directrix:

C) vertex: directrix:

D) vertex: directrix:

E) vertex: directrix:

Question 78

Identify the conic by writing the equation in standard form.

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

Question 79

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 80

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)