Deck 9: Conic Sections Systems of Non-Linear Equations

Question 1

Graph the system of equations, and use the graph to estimate the solutions.

-

A)
B)
C)
D)
E) None of these

Answer 1

Question 2

Graph the system of equations, and use the graph to estimate the solutions.

-

A)
B)
C)
D)
E) None of these

Answer 2

Question 3

Graph the system of equations, and use the graph to estimate the solutions.

-

A)
B)
C)
D) no real solution
E) None of these

Answer 3

Question 4

Graph the system of equations, and use the graph to estimate the solutions.

-

A)
B)
C)
D) no real solution
E) None of these

Question 5

Solve the system of equations by substitution.

-

A)
B)
C)
D)
E) None of these

Question 6

Solve the system of equations by substitution.

-

A)
B)
C)
D)
E) None of these

Question 7

Solve the system of equations by substitution.

-

A)
B)
C)
D)
E) None of these

Question 8

Solve the system of equations by substitution.

-

A)
B)
C)
D)
E) None of these

Question 9

Solve the system of equations by substitution.

-

A)
B)
C)
D) no real solution
E) None of these

Question 10

Solve the system of equations by elimination.

-

A)
B)
C)
D)
E) None of these

Question 11

Solve the system of equations by elimination.

-

A)
B)
C)
D) no real solution
E) None of these

Question 12

Solve the system of equations by elimination.

-

A)
B)
C)
D) no real solution
E) None of these

Question 13

Solve the system of equations by elimination.

-

A)
B)
C)
D)
E) None of these

Question 14

Solve the system of equations by elimination.

-

A)
B)
C)
D) no real solution
E) None of these

Question 15

For all the hyperbolas in these questions the center of the hyperbola is (0 ,0 ) .
The vertex of a hyperbola is (7,0) , the focus is (8,0) , and the transverse axis is y = 0 .

-Identify a, p and b.

A)
B)
C)
D)
E) None of these

Question 16

For all the hyperbolas in these questions the center of the hyperbola is (0 ,0 ) .
The vertex of a hyperbola is (7,0) , the focus is (8,0) , and the transverse axis is y = 0 .

-Write the equation of the hyperbola.

A)

B)

C)

D)

E) None of these

Question 17

For all the hyperbolas in these questions the center of the hyperbola is (0, 0).
The vertex is ( 0, -2) , the focus is (0, 4) , and the transverse axis is x= 0 .

-Identify a, p, and b.

A)
B)
C)
D)
E) None of these

Question 18

For all the hyperbolas in these questions the center of the hyperbola is (0, 0).
The vertex is ( 0, -2) , the focus is (0, 4) , and the transverse axis is x= 0 .

-Write the equation of the hyperbola.

A)
B)
C)
D)
E) None of these

Question 19

For all the hyperbolas in these questions the center of the hyperbola is (0, 0) .
The foci of a hyperbola are (-9, 0) and (9, 0) , and the vertex is ( -6, 0) .

-Identify a, p, and b.

A)
B)
C)
D)
E) None of these

Question 20

For all the hyperbolas in these questions the center of the hyperbola is (0, 0) .
The foci of a hyperbola are (-9, 0) and (9, 0) , and the vertex is ( -6, 0) .

-Write the equation of the hyperbola.

A)
B)
C)
D)
E) None of these

Question 21

For all the hyperbolas in these questions the center of the hyperbola is (0, 0) .
Use the equation of a hyperbola to answer the questions. Do not round irrational coordinates.

-Identify the foci.

A)
B)
C)
D)
E) None of these

Question 22

For all the hyperbolas in these questions the center of the hyperbola is (0, 0) .
Use the equation of a hyperbola to answer the questions. Do not round irrational coordinates.

-Identify the vertices.

A)
B)
C)
D)
E) None of these

Question 23

For all the hyperbolas in these questions the center of the hyperbola is (0, 0) .
Use the equation of a hyperbola to answer the questions. Do not round irrational coordinates.

-Identify the foci.

A)
B)
C)
D)
E) None of these

Question 24

For all the hyperbolas in these questions the center of the hyperbola is (0, 0) .
Use the equation of a hyperbola to answer the questions. Do not round irrational coordinates.

-Identify the vertices.

A)
B)
C)
D)
E) None of these

Question 25

For all the hyperbolas in these questions the center of the hyperbola is (0, 0) .

-The foci of a hyperbola are And , and the vertices are and . Identify a, b, and p.

A)
B)
C)
D)
E) None of these

Question 26

For all the hyperbolas in these questions the center of the hyperbola is (0, 0) .

-The foci of a hyperbola are and , and the vertices are And . Identify a, b, and p.

A)
B)
C)
D)
E) None of these

Question 27

For all the hyperbolas in these questions the center of the hyperbola is (0, 0) .

-For the hyperbola write the equations of the asymptotes.

A)
B)
C)
D)
E) None of these

Question 28

For all the hyperbolas in these questions the center of the hyperbola is (0, 0) .

-For the hyperbola write the equations of the asymptotes.

A)
B)
C)
D)
E) None of these

Question 29

Use the parabola to answer the questions.

-Identify the vertex.

A)
B)
C)
D)
E) None of these

Question 30

Use the parabola to answer the questions.

-Write the equation of the axis of symmetry.

A)
B)
C)
D)
E) None of these

Question 31

Use the parabola to answer the questions.

-Identify the vertex.

A)
B)
C)
D)
E) None of these

Question 32

Use the parabola to answer the questions.

-Write the equation of the axis of symmetry.

A)
B)
C)
D)
E) None of these

Question 33

Use the parabola to answer the questions.

-Identify the focus.

A)
B)
C)
D)
E) None of these

Question 34

Use the parabola to answer the questions.

-Write the equation of the directrix.

A)
B)
C)
D)
E) None of these

Question 35

Use the parabola to answer the questions.

-Identify the focus.

A)
B)
C)
D)
E) None of these

Question 36

Use the parabola to answer the questions.

-Write the equation of the directrix.

A)
B)
C)
D)
E) None of these

Question 37

Graph the parabola

A)
B)
C)
D)
E) None of these

Question 38

Graph the parabola

A)
B)
C)
D)
E) None of these

Question 39

Write the equation of the parabola with the given vertex, point on the parabola, and axis of symmetry.

-Vertex ; point ;

A)
B)
C)
D)
E) None of these

Question 40

Write the equation of the parabola with the given vertex, point on the parabola, and axis of symmetry.

-Vertex ; point ;

A)
B)
C)
D)
E) None of these

Question 41

Write the equation of the parabola with the given vertex, point on the parabola, and axis of symmetry.

-Vertex ; point ;

A)
B)
C)
D)
E) None of these

Question 42

For the parabola use interval notation to represent the domain and range.

A)
B)
C)
D)
E) None of these

Question 43

The headlight of an automobile is parabolic in shape. If the diameter is 4 inches and the depth is 1 inch, find the distance on the axis of symmetry from the vertex to the focus.

A) 4 in.
B) 0.5 in.
C) 2 in.
D) 1 in.
E) None of these

Question 44

The center of an ellipse is (0, 0) . The major axis is horizontal, and the distance between vertices on the major axis is 24. The minor axis is vertical, and the distance between vertices on the minor axis is 8.

-Identify the vertices.

A)
B)
C)
D)
E) None of these

Question 45

The center of an ellipse is (0, 0) . The major axis is horizontal, and the distance between vertices on the major axis is 24. The minor axis is vertical, and the distance between vertices on the minor axis is 8.

-Write the equation of the ellipse in standard form.

A)
B)
C)
D)
E) None of these

Question 46

The center of an ellipse is (4, -2) . The major axis is vertical, and the distance between the vertices on the major axis is 18. The minor axis is horizontal, and the distance between the vertices on the minor axis is 10. Identify the vertices.

A)
B)
C)
D)
E) None of these

Question 47

The center of an ellipse is (4, -2) . The major axis is vertical, and the distance between the vertices on the major axis is 20. The minor axis is horizontal, and the distance between the vertices on the minor axis is 14. Write the equation of the ellipse in standard form.

A)
B)
C)
D)
E) None of these

Question 48

Use the equation

-Rewrite the equation of the ellipse in standard form.

A)
B)
C)
D)
E) None of these

Question 49

Use the equation

-Identify the vertices of the major axis.

A)
B)
C)
D)
E) None of these

Question 50

Use the equation

-Identify the vertices of the minor axis.

A)
B)
C)
D)
E) None of these

Question 51

Sketch the graph of the ellipse

A)
B)
C)
D)
E) None of these

Question 52

Sketch the graph of the ellipse with the equation

A)
B)
C)
D)
E) None of these

Question 53

The major axis of an ellipse is horizontal, and the vertices of the major axis are and . The minor axis is vertical, and the vertices of the minor axis are and . Write the equation of the major axis.

A)
B)
C)
D)
E) None of these

Question 54

The major axis of an ellipse is horizontal, and the vertices of the major axis are and . The minor axis is vertical, and the vertices of the minor axis are and . Write the equation of the minor axis.

A)
B)
C)
D)
E) None of these

Question 55

The major axis of an ellipse is horizontal, and the vertices of the major axis are and . The minor axis is vertical, and the vertices of the minor axis are and . Identify the center.

A)
B)
C)
D)
E) None of these

Question 56

The major axis of an ellipse is horizontal, and the vertices of the major axis are and . The minor axis is vertical, and the vertices of the minor axis are and . Write the equation in standard form.

A)
B)
C)
D)
E) None of these

Question 57

An elliptical stained glass window is made to fit perfectly into a rectangular window frame so that the major and minor axis fit into the window frame without space between the stained glass and the frame. The major axis is 40 inches long and is vertical, and the minor axis is 28 inches long and is horizontal. If the center of the ellipse is , write an equation in standard form that is a model of this ellipse.

A)
B)
C)
D)
E) None of these

Question 58

The Mormon Tabernacle in Salt Lake City is an ellipse that is 250 feet by 150 feet. If the center is and the major axis is horizontal, write an equation in standard form that is a model of this ellipse.

A)
B)
C)
D)
E) None of these

Question 59

The two legs of a right triangle measure 6 in. and 7 in. Find the exact length of the hypotenuse. Do not round.

A)
B)
C)
D)
E) None of these

Question 60

Use the distance formula to find the exact distance between the points (15, -2) and ( -3, 13) .

A)
B)
C)
D) 2
E) None of these

Question 61

The lower left vertex of a square is the point (3, -2) . The upper left vertex of the square is the point (3, 7) . Find the other two vertices of this square.

A)
B)
C)
D)
E) None of these

Question 62

The three sides of an equilateral triangle have the same length. Two of the vertices of the triangle are (0, 5) and (4, -1) . Find the perimeter of this triangle.

A)
B)
C)
D)
E) None of these

Question 63

Find the midpoint of the line segment with the endpoints (-9 ,3) and (8, -5) .

A)
B)
C)
D)
E) None of these

Question 64

Write the equation in standard form of the circle with center (0, 0) and radius 4.

A)
B)
C)
D)
E) None of these

Question 65

Sketch the graph that represents the equation

A)
B)
C)
D)
E) None of these

Question 66

Write the equation in standard form of the circle with center (-8, 8) and radius 16.

A)
B)
C)
D)
E) None of these

Question 67

Write the equation in standard form of the circle with center (0, -7) and radius 9.

A)
B)
C)
D)
E) None of these

Question 68

Rewrite the equation of the circle in standard form.

A)
B)
C)
D)
E) None of these

Question 69

Find the center and the radius of the circle with the equatio

A)
B)
C)
D)
E) None of these

Question 70

Write the equation in standard form of the circle with center and passing through the point

A)
B)
C)
D)
E) None of these

Question 71

Solve the equation for y.

A)
B)
C)
D)
E) None of these

Question 72

The radius of the outer edge of a semi-circular window is 6 in. Write an equation that is a model of this window. Assume the origin is at the lower left corner of the window.

A)
B)
C)
D)
E) None of these

Question 73

The radius of the outer edge of the semicircular window pictured below is 16 in. Find the vertical distance between the top and bottom edges at a point that is 4 in. to the right of the midpoint of the bottom edge. Round to the nearest tenth.

A) 24.0 in.
B) 15.4 in.
C) 15.5 in.
D) 24.5 in.
E) None of these