CHAPTER 11 TEST B
Directions: Show all work.
Name: ______________________
Section: _____________________
1. Which one of the following formulas could describe the graph below?
a.
17 y  x 2  1
d.
y  x2  4
x2
 y2  1
b.
16
x2
 y2  1
e.
16
x2
y  1
4
y2
x2 
1
4
2
c.
f.
2. Which one of the following equations represents a parabola with focus at 16,0 ?
a.
x
d.
x
y2
4
b. x  
y2
4
e. x 
y2
16
y2
16
c.
x
f.
x
y2
64
y2
64
3. The ellipse with vertices at  3, 0  and  3, 16  , covertices at  6, 8 and  0, 8
is represented by which one of the following equations?
a. 64 x 2  9 y 2  384 x  144 y  576
b. x 2  y 2  6 x  8 y  0
c. 8x 2  3 y 2  48x  24 y  24
d. 64 x 2  9 y 2  96 x  36 y  144
e. x 2  y 2  6 x  8 y  0
f. 8x 2  3 y 2  48x  24 y  24
4. Which one of the following equations represents a hyperbola centered at 1,1 ,
vertices at  0,1 ,  2,1 and asymptotes y  1  2  x  1 ?
a.
 x  1
2
4
d.  x  1
2
  y  1  1
2
 y  1

4
Chapter 11/Form B
b.
2
1
e.
 x  1
2
2
 x  1
2
  y  1  1
2
 y  1

2
c.
2
1
f.
 y  1
2
 y  1
2
 x  1

2
1
4
2
  x  1  1
2
5. Which one of the following shows the solution to the system of inequalities:
18  x  3 y  6
3 y 7
0 x6
a.
b.
c.
d.
6. Information about the age distributions in three different villages (A, B and C) is
given in the box plots shown below. Which one of the following statements about
these trees below is not true?
a.
b.
c.
d.
e.
The youngest person lives in village C.
Inhabitants of village A have the youngest median age.
The median age of village A is greater than the first quartile age of village B.
One quarter of people in village B are older than the oldest person in village A.
One quarter of the inhabitants of village C are less than ten years of age.
Chapter 11/Form B
7. Find the lengths of the major and minor axes and the coordinates of the foci for the
x2 y 2
ellipse described by the equation

 1 and sketch a graph for the ellipse
36 49
showing these features.
8. Find coordinates for the points on the ellipse
 x  4
48
2

y2
 1 where x  2 .
9
9. Find the coordinates of the vertices and the equations for the asymptotes of
x2
y2

 1 and use these to sketch a graph of the hyperbola.
144 324
10. Find an equation for the parabola with a vertex at the origin and a focus at  0, 8 .
Sketch a graph for the parabola showing these features together with the directrix.
11. Find an equation for the parabola with a vertex at  2,3 and a focus at  5,3 .
Sketch a graph for the parabola showing these features together with the directrix.
12. Find the coordinates of the focus and an equation for the directrix of the parabola
2
described by x  3  y  2   1 . Sketch a graph for the parabola showing these
features.
13. Find the center and the lengths of the major and minor axes of the ellipse described
1
1
by the equation x 2  9 y 2  x  . Sketch a graph for the ellipse showing these
4
8
features.
14. Find the center, vertices and asymptotes for the hyperbola given by the equation
36 x 2  24 x  324 y 2  324 y  401
15. Find an equation for hyperbola shown below:
Chapter 11/Form B
Problems 16-20 refer to the linear programming problem in the following situation:
The manager of a software retailer has asked her assistant for a cost analysis to
help determine what software they will order. They are choosing between two types of
database packages: Stackmaker, and a more expensive full-featured package called
Deluxstack. The assistant must figure out how many packages of each software to order
to minimize costs. It is required that they sell at least 300 packages (some combination
of Stackmaker and Deluxstack.) A Stackmaker sale earns $18 in profit for the retailer,
while a Deluxstack sale earns $24 in profit. Total profits on database software sales
must be at least $6240. The wholesale cost of Stackmaker is $25. The wholesale cost
Deluxstack is $40. The retailer buys software at the wholesale cost.
16. Let s represent the number of Stackmaker packages the retailer will order and let d
represent the number of packages of Deluxstack the company will order. Write the
constraints of the problem as inequalities in terms of s and d.
17. Write the objective function of the problem in terms of s and d.
18. Sketch the solution set to the constraint system.
19. Find the coordinates of the vertices of the solution set.
20. Find the combination of Stackmaker and Deluxstack packages that will minimize
cost. What is this minimum cost?
21. Approximate to four significant digits the coordinates of the foci of the hyperbola
given by
 x  3
2
2
 y  4

2
2

6 2
.
2
22. The equation y 2  2 xy  2 x 2  1 can be solved for y using the quadratic formula.
For a given x there may be two solutions: y  x  3x 2  1. Graph these two
functions on a calculator and describe what you see in terms of a conic section.
23. Approximate to 4 significant digits the value(s) of x in the solution(s) to the system:
2
x2  4  y  2  4
.
2
y  0.2  x  2 
Chapter 11/Form B
Problems 24 and 25 refer to the following linear programming problem:
:
x
y
maximize

2  1.4
3  1.7
 3  2 y  5x  6
such that
 7  2 2 y  3 x  10
24. Approximate to four significant digits the vertices of the solution region for the
constraint system. Sketch a graph of the constraint system to show these.
25. Find the maximum value of
constraint system.
Chapter 11/Form B
x
y
over the solution set of the

2  1.4
3  1.7
Solutions For Chapter 11 Test Form B.
1. b 2. f
3. a 4. d 5. b 6. d
7. The major axis has length 14 and the minor axis
has length 12 while the foci are at 0,  13 .

8.
 2  4
2
y2
y2 1
3
1
  y
48
9
9 4
2
3

 coordinates at  2,   .
2


9. The vertices of the hyperbola are at
 12,0 and the asymptotes are
3
x , as shown to the right:
2
x2
10. y  
is an equation for the parabola.
32
The graph is shown below:
y
11. The equation for the parabola
1
2
is x  2   y  3 . The
28
directrix is x  9 . The
graph is shown below to the
right:
Chapter 11/Form B

12. The vertex of x  3  y  2   1 is at  1, 2  and
2
the distance to the focus is p 
1
so the focus
12
 11 
is at   , 2  and the directrix is
 12 
A graph is shown at right:
x
13 .
12
2
13. x 2  9 y 2 
1
1
1
1 1

x    x    9 y2  
.
4
8
8
8 64

2
1

x 
8

 64 y 2  1 So the length of the
9 / 64
9 3
 and the length
16 2
1 1
of the minor axis is 2a  2
 . The
64 4
 1 
ellipse is centered at   , 0  as shown:
 8 
2
2
14. 36 x  24 x  324 y  324 y  401
2 

 36  x 2  x   324  y 2  y   401
3 

major axis is 2a  2
2
2
1
1


 36  x    324  y    401  4  81
3
2


2
1

2
x 
1
3 

  y    1 . So the center is
9
2

1   10 1 
1 1
1
 8 1
at  ,  , the vertices are at   3,    ,  and   ,  and the asymptotes
2  3 2
3 2
3
 3 2
1
1
1
1
7
11 1
and y   x .
are y     x    y  x 
2
3
3
3
18
18 3
 y  2
2
 x  3

2
 1 , observe that the points  3, 1 and
b2
a2
(0,0) are on the hyperbola so that b  1 and a  3 . Thus an equation for the
15. Starting with the form
hyperbola is  y  2 
Chapter 11/Form B
2
 x  3

3
2
1.
s  d  300
16. The constraint system is 18s  24d  6240 .
s, d  0
17. The cost function, C  25s  40d , is to be
minimized.
18. See sketch to the right:
19. As shown in the illustration, the vertices of
2

the solution set are  0,346  , 140,160 and  300, 0  .
3

2

20. The cost function is minimized at  0,346  where C = $ 8666.67
3

21. The foci are at  3  c, 4  where c  1  2  3  6 
Thus the foci are near  5.568, 4  and  0.432, 4  .
22. These two functions comprise a hyperbola whose
axes are tilted and whose center is near the origin,
as shown at right.
23. Plotting the three functions involved and using the
“ISECT” feature on the TI85 shows that there appears
to be only one point of
intersection near where
x  1.769
24. As the screenshots at right show,
the feasible region is a rhombus
with vertices near
 0.9107,0.1521 ,
 0.9915,0.1162 ,
 0.04898,1.170 , and
 0.03185, 0.9016 .
25. Evidently, the maximum value of
the object function is about 68.81
and is attained near
 0.9107,0.1521 .
Chapter 11/Form B
1  2 1  3   2.568