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MAC 1140 Module 11 Test
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Match the graph of the parabola with the appropriate equation.
1)
y
10
5
-10
-5
5
10 x
-5
-10
A) x = (y - 2)2 - 2
B) y = (x - 2)2 - 2
C) y = (x + 2)2 + 2
Answer: A
Objective: (10.1) Match Graph of Parabola with Equation
Find the vertex, focus, and directrix of the parabola.
2) x2 = 4y
A) Vertex: V(0, 0); focus: F(0, 1), directrix: y = -1
B) Vertex: V(0, 0); focus: F(1, 0); directrix: y = 1
C) Vertex: V(0, 0); focus: F(0, -1); directrix: x = - 1
D) Vertex: V(0, 0); focus: F(1, 0); directrix: x = 1
Answer: A
Objective: (10.1) Find Vertex, Focus, and Directrix of Parabola
1
D) x = (y + 2)2 - 2
Find the equation of the parabola corresponding to the given information.
3) The parabola has focus and directrix as shown.
y
10
5
-10
-5
5
-5
10 x
F
-10
B) y = - 1 x2
16
A) y = - x2
C) y = 1 x2
16
D) x = 1 y 2
16
C) y = x2 + 3
D) y = x2 - 3
C) -8y = x2
D) y = 1 x2
8
Answer: B
Objective: (10.1) Find Equation of Parabola with Vertex at Origin
Match the graph of the parabola with the appropriate equation.
4)
y
10
5
-10
-5
5
10 x
-5
-10
A) x = y 2 + 3
B) x = y 2 - 3
Answer: A
Objective: (10.1) Match Graph of Parabola with Equation
Find an equation of a parabola satisfying the given conditions.
5) Focus at (2, 0), directrix x = -2
A) y 2 = -8x
B) x = 1 y 2
8
Answer: B
Objective: (10.1) Find Equation of Parabola that Satisfies Conditions
2
Solve the problem.
6) A radio telescope has a parabolic surface. If it is 1 m deep and 12 m wide, how far is the focus from the
vertex?
A = 12 m
B= 1m
A) 36 m
B) 3 m
C) 9 m
D) 1 m
Answer: C
Objective: (10.1) Solve Apps: Parabolas
Graph the parabola.
7) -8x = y 2
y
10
5
-10
-5
10 x
5
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
5
-5
-5
-10
-10
3
10 x
C)
D)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
5
-5
-5
-10
-10
Answer: D
Objective: (10.1) Graph the Parabola
Find an equation for the indicated ellipse.
8) Center (3, 7), focus (3, 8), and vertex (3, 12)
2
2
A) (x - 3) + (y - 7) = 1
24
26
2
2
B) (x - 3) + (y - 7) = 1
24
25
2
2
C) (x + 3) + (y + 7) = 1
25
24
2
2
D) (x + 3) + (y + 7) = 1
24
25
Answer: B
Objective: (10.2) Find Equation of Ellipse with Center Not at Origin
4
10 x
Graph the ellipse satisfying the stated conditions.
9) The equation is 9x2 + y 2 = 9.
A)
B)
y
y
4
4
3
3
2
2
1
1
-4 -3 -2 -1
-1
1
2
3
4
x
-4 -3 -2 -1
-1
-2
-2
-3
-3
-4
-4
C)
1
2
3
4
x
1
2
3
4
x
D)
y
y
4
4
3
3
2
2
1
1
-4 -3 -2 -1
-1
1
2
3
4
x
-4 -3 -2 -1
-1
-2
-2
-3
-3
-4
-4
Answer: A
Objective: (10.2) Graph Ellipse with Center at Origin
Shade the region in the xy-plane that satisfies the system of inequalities.
2
2
10) x + y ≤ 1
100
64
-x + y ≥ 3
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
2
4
6
8 10 x
5
A)
B)
y
y
10
8
6
4
2
10
8
6
4
2
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
C)
2
4
6
8 10 x
2
4
6
8 10 x
D)
y
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
10
8
6
4
2
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
Answer: D
Objective: (10.2) Graph Nonlinear System of Inequalities
Identify the vertices and foci.
2
2
11) (x + 5) + (y + 2) = 1
100
64
A) Vertices: (-2, -15), (-2, 5); Foci: (-2, -13), (-2, 3)
B) Vertices: (-15, -2), (5, -2); Foci: (-13, -2), (3, -2)
C) Vertices: (-15, -2), (5, -2); Foci: (-11, -2), (1, -2)
D) Vertices: (-2, -15), (-2, 5); Foci: (-2, -11), (-2, 1)
Answer: C
Objective: (10.2) Find Foci andVertices of Ellipse (Center Not at Origin)
6
Solve the problem.
12) A railroad tunnel is shaped like a semiellipse. The height of the tunnel at the center is 48 ft and the vertical
clearance must be 24 ft at a point 24 ft from the center. Find an equation for the ellipse.
2
2
A) x + y = 1
576
2304
2
2
B) x + y = 1
768
576
2
2
C) x + y = 1
2304
768
2
2
D) x + y = 1
768
2304
Answer: D
Objective: (10.2) Solve Apps: Ellipses
Graph the ellipse satisfying the stated conditions.
13) Vertices at ( ±8 , 0 ) and eccentricity 1
2
A)
B)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
C)
5
10 x
5
10 x
D)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
Answer: A
Objective: (10.2) Graph Ellipse with Center at Origin
Find the center and radius of the circle.
14) x2 + y 2 - 4x - 14y = -17
A) (-2, -7), r = 36
B) (-7, -2), r = 36
C) (2, 7), r = 6
Answer: C
Objective: (10.2) Find Center and Radius of Circle from Equation
7
D) (7, 2), r = 6
Graph the equation.
2
2
15) x - y = 1
4
25
y
10
5
-10
-5
10 x
5
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
C)
5
10 x
5
10 x
D)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
Answer: B
Objective: (10.3) Graph Hyperbola with Center at Origin
8
Solve the problem. Round to the nearest tenth.
16) The roof of a building is in the shape of the hyperbola 5y 2 - x2 = 55, where x and y are in meters. Refer to
the figure and determine the height, h, of the outside walls.
a=b=4m
A) 71 m
B) 3.8 m
C) 14.2 m
D) 8.4 m
2
2
C) y - x = 1
144
16
2
2
D) y - x = 1
16
36
Answer: B
Objective: (10.3) Solve Apps: Hyperbolas
Find the equation of the hyperbola satisfying the given conditions.
17) Vertices at (0, ±4); asymptotes y = ± 1 x
3
2
2
A) y - x = 1
16
144
2
2
B) y - x = 1
36
4
Answer: A
Objective: (10.3) Find Equation of Hyperbola Given Conditions
Graph the hyperbola.
2
2
18) (x + 5) - (y + 1) = 1
4
64
y
10
5
-10
-5
5
10
x
-5
-10
9
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
x
5
10
x
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
Answer: C
Objective: (10.3) Graph Hyperbola with Center Not at Origin
Solve the system of equations.
19) x2 - 3y 2 = 1
4x2 + 3y 2 = 19
A) (2, 1), (2, -1), (-2, 1), (-2, -1)
C) (2, 1) and (-2, -1)
B) (-1, 2) and (1, -2)
D) (1, 2), (-1, 2), (1, -2), (-1, -2)
Answer: A
Objective: (10.3) Solve Nonlinear System of Equations
10
Match the given equation with one of the graphs.
20) 4x2 - 36y 2 = 144
A)
B)
y
y
x
x
C)
D)
y
y
x
x
Answer: D
Objective: (10.3) Match Equation of Hyperbola with Graph
11