Deck 9: Conic Sections

Question 1

Identify the center and radius of the circle.

Answer 1

B

Question 2

Write the word or phrase that best completes each statement or answers the question.
Find all values of k so that the distance from (-10, 6) to (-7, k) is 5 units.

Answer 2

k = 2 or 10

Question 3

Determine if the three points define the vertices of a right triangle. (-1, -2), (-5, 6), (7, 2)

A) Yes
B) No

Answer 3

A

Question 4

Write the word or phrase that best completes each statement or answers the question.
Write an equation of a circle whose center is (20, 4) and that passes through the point (21, -5).

Question 5

Use the distance formula to find the distance between the two points. (4, 0) and (0, -7)

A) 65
B) 11
C)
D) 3

Question 6

Use the distance formula to find the distance between the two points. (-3, 18) and (-3, -6)

A) -12
B) 24
C) 12
D) -24

Question 7

Write the word or phrase that best completes each statement or answers the question.
Write an equation of a circle centered at (10, -2) with a radius of 10.

Question 8

Identify the center and radius of the circle.

Question 9

Identify the center and radius of the circle.

Question 10

Question 11

Which of the following is the equation of a circle?

Question 12

Write the word or phrase that best completes each statement or answers the question.
Identify the center and radius of the circle and then graph the circle.

Question 13

Use the distance formula to find the distance between the two points. (-2, 18) and (4, 10)

A) 10
B) 14
C) 100
D)

Question 14

Identify the center and radius of the circle.

Question 15

Write the word or phrase that best completes each statement or answers the question.
Write the distance formula.

Question 16

Write an equation that represents the graph of the circle.

Question 17

Find the midpoint of the line segment. (You can check your answer by plotting the midpoint on the graph).

Question 18

Use the distance formula to find the distance between the two points. (2, 6) and (-2, 14)

Question 19

Write an equation of a circle centered at (-2, -8) with a diameter of 2.

Question 20

Write the word or phrase that best completes each statement or answers the question.
Identify the center and radius of the circle and then graph the circle.

Question 21

Determine the vertex by using the vertex formula.

Question 22

Use the equation of the parabola in standard form y = a(x - h)2 + k to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph
The parabola.

Question 23

Use the equation of the parabola in standard form y = a(x - h)2 + k to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph
The parabola.

Question 24

Use the equation of the parabola in standard form to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph
The parabola.

Question 25

Use the equation of the parabola in standard form to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph
The parabola.

Question 26

The cross sections of a certain satellite dish are parabolic in shape. A cross section through the vertex can be described by the equation where d(x) is the depth of the dish (in feet) at a distance of x ft from the edge of the dish. How deep
Is the satellite dish?

Question 27

Use the equation of the ellipse to identify the center (h, k).

Question 28

Write the word or phrase that best completes each statement or answers the question.
Find the x- and y-intercepts of the ellipse

Question 29

Find the midpoint of the line segment between the two given points. (1, -2) and (-9, 2)

A) (-8, 0)
B) (-2, 5)
C) (-3, 1)
D) (-4, 0)

Question 30

Use the equation of the parabola first to determine whether the axis of symmetry is vertical or horizontal. Then determine if the parabola opens upward, downward, left, or right.

A) Vertical axis of symmetry;
B) Horizontal axis of symmetry; opens downward opens right
C) Vertical axis of symmetry;
D) Horizontal axis of symmetry; opens upward opens left

Question 31

Use the equation of the parabola first to determine whether the axis of symmetry is vertical or horizontal. Then determine if the parabola opens upward, downward, left, or right.

A) Horizontal axis of symmetry;
B) Vertical axis of symmetry; opens left opens downward
C) Vertical axis of symmetry;
D) Horizontal axis of symmetry; opens upward opens right

Question 32

Use the equation of the parabola in standard form to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph
The parabola.

Question 33

Find the center of a circle if a diameter of the circle has endpoints (-5, -4) and (-11, -2).

A) (-8, -3)
B) (3, -1)
C) (3, -3)
D) (-8, -1)

Question 34

A map of a hiking area is drawn so that the Visitor Center is at the origin of a rectangular grid. Two hikers are located at positions (-3, 1) and (2, 3) with respect to the Visitor Center where all units are in
Miles. A campground is located exactly halfway between the hikers. What are the coordinates of the
Campground?

Question 35

Find the midpoint of the line segment between the two given points. (-0.2, -4.5) and (-3.7, -2.1)

A) (1.75, -1.2)
B) (-2.35, -2.9)
C) (-1.95, -1.2)
D) (-1.95, -3.3)

Question 36

Use the equation of the parabola in standard form to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph
The parabola.

Question 37

Find the x- and y-intercepts of the ellipse = 1 and graph the ellipse.

Question 38

Find the midpoint of the line segment between the two given points. (-4, -6) and (2, -10)

A) (-1, -8)
B) (-8, -1)
C) (-5, -4)
D) (-2, -16)

Question 39

Determine the vertex by using the vertex formula.

A) (-6, 9)
B) (-6, -9)
C) (9, -6)
D) (-9, -6)

Question 40

Identify the center of the ellipse Then graph the ellipse.

Question 41

Give the coordinates of the vertices for the following hyperbola.

Question 42

Sketch the system of equations. Then solve the system by the substitution method.

Question 43

Graph the hyperbola centered at (h, k) by following these guidelines. First locate the center. Then
draw the reference rectangle relative to the center (h, k). Using the reference rectangle as a guide, sketch
the hyperbola.

Question 44

Solve the system by the substitution method.

Question 45

Write the word or phrase that best completes each statement or answers the question.
Determine whether the transverse axis of the hyperbola is horizontal or vertical.

Question 46

Write the word or phrase that best completes each statement or answers the question.
Solve the system by the substitution method.

Question 47

Determine whether the transverse axis of the hyperbola is horizontal or vertical.

Question 48

Solve the system of nonlinear equations by the substitution method.

Question 49

Give the coordinates of the vertices for the following hyperbola. [The fundamental rectangle and asymptotes are shown in dashed lines.]

A) (6, 5), (6, -1), (-4, -1), and (-4, 5)
B) (1, 2)
C) (5, 1) and (-1, 1)
D) (1, 5) and (1, -1)

Question 50

Identify the center of the ellipse Then graph the ellipse.

Question 51

Determine if the equation represents an ellipse or a hyperbola.

A) Ellipse
B) Hyperbola

Question 52

Determine if the equation represents an ellipse or a hyperbola.

A) Hyperbola
B) Ellipse

Question 53

Solve the system by the addition method.

Question 54

Write the word or phrase that best completes each statement or answers the question.
Use the equation in standard form to graph the hyperbola.

Question 55

Solve the system of nonlinear equations by the addition method.

Question 56

Solve the system of nonlinear equations by the addition method.

Question 57

Sketch the system of equations. Then solve the system by the substitution method.

Question 58

Solve the system of nonlinear equations by the addition method.

Question 59

Sketch the system of equations. Then solve the system by the substitution method.

Question 60

Solve the system by the substitution method.

Question 61

Graph the solution set.

Question 62

Graph the solution set.

Question 63

Solve the system of nonlinear equations by the addition method.

Question 64

Graph the solution set to the system of inequalities.

Question 65

Write the word or phrase that best completes each statement or answers the question.
Describe the solution set for the inequality.

Question 66

Graph the solution set.

Question 67

The sum of two numbers is 13. The sum of the squares of the numbers is 109. Find the numbers.

A) 5 and 8
B) 3 and 10
C) 0 and 13
D) 4 and 9

Question 68

Solve the system of nonlinear equations by the addition method.

Question 69

Graph the solution set to the system of nonlinear inequalities.

Question 70

Solve the system of nonlinear equations by the addition method.

Question 71

A coordinate system is placed at the center of a house with the positive x-axis pointing east, and the positive y-axis pointing north. A pest-deterrent device that uses high-frequency sound waves is
Placed in an electrical outlet 15 ft west and 8 ft south of the center of the house. If the device has a
Range of 11 feet, write an inequality that represents the points on the coordinate system affected by
The device.

Question 72

Graph the solution set to the system of nonlinear inequalities.

Question 73

Write the word or phrase that best completes each statement or answers the question.
Graph the solution set to the system of nonlinear inequalities.

Question 74

How would the solution set for change for the strict inequality

Question 75

Graph the solution set.

Question 76

Graph the solution set to the system of nonlinear inequalities.

Question 77

The point (5, 1) satisfies the inequality.

A) False
B) True

Question 78

Graph the solution set to the system of inequalities.

Question 79

Graph the solution set.

Question 80

Describe the solution set for the inequality.