QUIZ Group Member: Hamza,Ameera Hanan Casco, Mariane Nicole Tapel, Rona Jane

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1
Situational Problem
Involving Conic
Sections
QUIZ 5
SUMMATIVE TEST

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LET’S START,
GOODLUCK!
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PART I
Determine whether each of
the following terms is related
to CIRCLE, PARABOLA,
HYPERBOLA, or ELLIPSE.
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1. (x-h)2+(y-k)2= r2
A. CIRCLE
B. PARABOLA
C. HYPERBOLA
D. ELLIPSE

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2. 𝑥−ℎ 2
𝑎2 −
𝑦−𝑘 2
𝑏2 = 1
A. CIRCLE
B. PARABOLA
C. HYPERBOLA
D. ELLIPSE

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6 6
3.
𝑦−ℎ 2
𝑎2 +
𝑦−𝑘 2
𝑏2 = 1
A. CIRCLE
B. PARABOLA
C. HYPERBOLA
D. ELLIPSE

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7 7
4. y= 4p(x-h)2
A. CIRCLE
B. PARABOLA
C. HYPERBOLA
D. ELLIPSE

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5. FOCUS
A. CIRCLE
B. PARABOLA
C. HYPERBOLA
D. ELLIPSE

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PART II
Direction. Write the letter of your
choice. If the answer is not among
the given choices, write your answer.

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For items 1 to 3, refer to the following scenario:
A stadium is shaped as in the figure below where its left and right
end are circular arcs both with center at C. What is the length of the
stadium 50 m from one of the straight sides?
1. Which of the following could be the
radius of the left side circle (smaller
circle)?
A. 50m
B. 100m
C. 150m
D. 200m

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11
For items 1 to 3, refer to the following scenario:
A stadium is shaped as in the figure below where its left and right
end are circular arcs both with center at C. What is the length of the
stadium 50 m from one of the straight sides?
2. Which of the following could be the
equation of the left side circle if Point C is
the center (0,0)?
A. 𝑥2+𝑦2=502
B. 𝑥2
+𝑦2
=1002
C. 𝑥2
+𝑦2
=1502
D. 𝑥2+𝑦2=2002

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12
12
For items 1 to 3, refer to the following scenario:
A stadium is shaped as in the figure below where its left and right
end are circular arcs both with center at C. What is the length of the
stadium 50 m from one of the straight sides?
3. Which of the following could be the
radius of the right-side circle (largest
circle)?
A. √1,000
B. √10,000
C. √100,000
D. √1,000,000

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13
For items 4 to 6, refer to the following scenario:
A satellite dish has a shape called a paraboloid, where each cross-section is a
parabola. Since radio signals (parallel to the axis) will bounce off the surface of
the dish to the focus, the receiver should be placed at the focus. How far should
the receiver be from the vertex, if the dish is 12 ft across, and 4.5 ft deep at the
vertex?
4. Which of the following is NOT the
reason why (6, 4, 5) is a point in the
parabola?
A. The center is the origin
B. 12 ft across were divided by right & left side
C. The height is 4.5
D. The receiver is in the vertex

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14
For items 4 to 6, refer to the following scenario:
A satellite dish has a shape called a paraboloid, where each cross-section is a
parabola. Since radio signals (parallel to the axis) will bounce off the surface of
the dish to the focus, the receiver should be placed at the focus. How far should
the receiver be from the vertex, if the dish is 12 ft across, and 4.5 ft deep at the
vertex?
5. What should be determined from
the problem?
A. The value of c
B. The focus
C. The value of y
D. The value of x

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15
For items 4 to 6, refer to the following scenario:
A satellite dish has a shape called a paraboloid, where each cross-section is a
parabola. Since radio signals (parallel to the axis) will bounce off the surface of
the dish to the focus, the receiver should be placed at the focus. How far should
the receiver be from the vertex, if the dish is 12 ft across, and 4.5 ft deep at the
vertex?
6. Where should the receiver be
located from the vertex?
A. 1ft away
B. 2ft away
C. 3ft away
D. 4ft away

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16
For items 7-10, refer to the following scenario:
An object thrown from a height of 2 m above the ground follows a parabolic path
until the object falls to the ground; see Figure below. If the object reaches a
maximum height (measured from the ground) of 7 m after traveling a horizontal
distance of 4 m, determine the horizontal distance between the object’s initial
and final positions.
7. The vertex of the parabola can be
A. (0,7)
B. (7,0)
A. (0,0)
B. (-4,2)

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17
For items 7-10, refer to the following scenario:
An object thrown from a height of 2 m above the ground follows a parabolic path
until the object falls to the ground; see Figure below. If the object reaches a
maximum height (measured from the ground) of 7 m after traveling a horizontal
distance of 4 m, determine the horizontal distance between the object’s initial
and final positions.
8. The equation of the parabola is
A. 𝑥2
= 4c(y-7)
B. 𝑥2
= -4c(y-7)
C. 𝑦2= 4c(x-7)
B. 𝑦2
= -4c(x-7)

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18
For items 7-10, refer to the following scenario:
An object thrown from a height of 2 m above the ground follows a parabolic path
until the object falls to the ground; see Figure below. If the object reaches a
maximum height (measured from the ground) of 7 m after traveling a horizontal
distance of 4 m, determine the horizontal distance between the object’s initial
and final positions.
9. The starting point of the object can
be viewed at which point?
A. (2, -4)
B. (-4, 2)
C. (-2, 4)
B. (4, -2)

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19
For items 7-10, refer to the following scenario:
An object thrown from a height of 2 m above the ground follows a parabolic path
until the object falls to the ground; see Figure below. If the object reaches a
maximum height (measured from the ground) of 7 m after traveling a horizontal
distance of 4 m, determine the horizontal distance between the object’s initial
and final positions.
10. In the parabola, if the value of c=
4
5
,
which of the following could be the
equation of the parabola?
A. 𝑥2 = 16
5
(𝑦−7)
B. 𝑥2 = -16
5
(𝑦−7)
C. 𝑦2= 16
5
(𝑥−7)
B. 𝑦2= -16
5
(𝑥−7)

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20
For items 11-12, refer to the following scenario:
A tunnel has the shape of semi ellipse that is 15ft at the center, and 36ft across
at the base. At how high should a passing truck be, if it 12ft wide, for it to be
able to fit through the tunnel? Round off your answer to two decimal places.
11. If the center is at (0,0), then which
of the following could be the equation
of the ellipse?
A.
𝑥2
182 +
𝑦2
152 = 1
B.
𝑥2
152 +
𝑦2
182 = 1
C.
𝑥2
62 +
𝑦2
152 = 1
B.
𝑥2
152 +
𝑦2
62 = 1

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21
For items 11-12, refer to the following scenario:
A tunnel has the shape of semi ellipse that is 15ft at the center, and 36ft across
at the base. At how high should a passing truck be, if it 12ft wide, for it to be
able to fit through the tunnel? Round off your answer to two decimal places.
12. From the problem, since the width of the
truck is 12ft, then which of the following is the
correct solution in finding the height of the
truck?
A. 𝑥2
182 + 𝑦2
152 = 1, so if x = 6, then 62
182 + 𝑦2
152 = 1, and thus y=10√2
B. 𝑥2
152 + 𝑌2
182 = 1, so if x = 6, then 62
152 + 𝑦2
152 = 1, and thus y=18√21
5
C. 𝑥2
62 + 𝑦2
152 = 1, so if x= 6, then 62
62 + 𝑦2
152 = 1, and thus y = 0
D. 𝑥2
152 + 𝑦2
6
= 1, so if x= 6, then 62
152 + 𝑦2
62 = 1, and thus y = 6√21
5
0

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22
For items 13-15, refer to the following scenario:
Two stations, located at M (-1.5, 0) and N (1.5, 0) (units are in km),
simultaneously send sound signals to a ship, with the signal traveling at the
speed of 0.33 km/s. if the signal from N was received by the ship four seconds
before the signal it received from M, find the equation of the curve containing
the possible location of the ship.
13. From the problem, how far in km are the two stations?
A. 1.50 B. 3.00 C. 1.32 D. 1.81

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23
For items 13-15, refer to the following scenario:
Two stations, located at M (-1.5, 0) and N (1.5, 0) (units are in km),
simultaneously send sound signals to a ship, with the signal traveling at the
speed of 0.33 km/s. if the signal from N was received by the ship four seconds
before the signal it received from M, find the equation of the curve containing
the possible location of the ship.
14. How far is the ship from point M in km?
A. 1.50 B. 3.00 C. 1.32 D. 1.81

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24
24
For items 13-15, refer to the following scenario:
Two stations, located at M (-1.5, 0) and N (1.5, 0) (units are in km),
simultaneously send sound signals to a ship, with the signal traveling at the
speed of 0.33 km/s. if the signal from N was received by the ship four seconds
before the signal it received from M, find the equation of the curve containing
the possible location of the ship.
15. Which of the following is the equation of the curve
containing the possible location of the ship?
A.
𝑥2
0.4356
-
𝑦2
1.8144
= 1 C.
𝑦2
0.4356
-
𝑥2
1.8144
= 1
B.
𝑥2
1.8144
-
𝑦2
0.5346
= 1 D.
𝑦2
1.8144
-
𝑥2
0.4356
= 1

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EXCHANGE
PAPER AND
LET’S CHECK!

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PART I ANSWER KEY

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1. (x-h)2+(y-k)2= r2
A. CIRCLE
B. PARABOLA
C. HYPERBOLA
D. ELLIPSE

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2. 𝑥−ℎ 2
𝑎2 −
𝑦−𝑘 2
𝑏2 = 1
A. CIRCLE
B. PARABOLA
C. HYPERBOLA
D. ELLIPSE

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3.
𝑦−ℎ 2
𝑎2 +
𝑦−𝑘 2
𝑏2 = 1
A. CIRCLE
B. PARABOLA
C. HYPERBOLA
D. ELLIPSE

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4. y= 4p(x-h)2
A. CIRCLE
B. PARABOLA
C. HYPERBOLA
D. ELLIPSE

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5. FOCUS
A. CIRCLE
B. PARABOLA
C. HYPERBOLA
D. ELLIPSE

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PART II ANSWER KEY

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33
For items 1 to 3, refer to the following scenario:
A stadium is shaped as in the figure below where its left and right
end are circular arcs both with center at C. What is the length of the
stadium 50 m from one of the straight sides?
1. Which of the following could be the
radius of the left side circle (smaller
circle)?
A. 50m
B. 100m
C. 150m
D. 200m

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34
34
For items 1 to 3, refer to the following scenario:
A stadium is shaped as in the figure below where its left and right
end are circular arcs both with center at C. What is the length of the
stadium 50 m from one of the straight sides?
2. Which of the following could be the
equation of the left side circle if Point C is
the center (0,0)?
A. 𝑥2+𝑦2=502
B. 𝑥2
+𝑦2
=1002
C. 𝑥2
+𝑦2
=1502
D. 𝑥2+𝑦2=2002

35. Click to edit Master title style
35
35
For items 1 to 3, refer to the following scenario:
A stadium is shaped as in the figure below where its left and right
end are circular arcs both with center at C. What is the length of the
stadium 50 m from one of the straight sides?
3. Which of the following could be the
radius of the right-side circle (largest
circle)?
A. √1,000
B. √10,000
C. √100,000
D. √1,000,000

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36
36
For items 4 to 6, refer to the following scenario:
A satellite dish has a shape called a paraboloid, where each cross-section is a
parabola. Since radio signals (parallel to the axis) will bounce off the surface of
the dish to the focus, the receiver should be placed at the focus. How far should
the receiver be from the vertex, if the dish is 12 ft across, and 4.5 ft deep at the
vertex?
4. Which of the following is NOT the
reason why (6, 4, 5) is a point in the
parabola?
A. The center is the origin
B. 12 ft across were divided by right & left side
C. The height is 4.5
D. The receiver is in the vertex

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37
37
For items 4 to 6, refer to the following scenario:
A satellite dish has a shape called a paraboloid, where each cross-section is a
parabola. Since radio signals (parallel to the axis) will bounce off the surface of
the dish to the focus, the receiver should be placed at the focus. How far should
the receiver be from the vertex, if the dish is 12 ft across, and 4.5 ft deep at the
vertex?
5. What should be determined from
the problem?
A. The value of c
B. The focus
C. The value of y
D. The value of x

38. Click to edit Master title style
38
38
For items 4 to 6, refer to the following scenario:
A satellite dish has a shape called a paraboloid, where each cross-section is a
parabola. Since radio signals (parallel to the axis) will bounce off the surface of
the dish to the focus, the receiver should be placed at the focus. How far should
the receiver be from the vertex, if the dish is 12 ft across, and 4.5 ft deep at the
vertex?
6. Where should the receiver be
located from the vertex?
A. 1ft away
B. 2ft away
C. 3ft away
D. 4ft away

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39
For items 7-10, refer to the following scenario:
An object thrown from a height of 2 m above the ground follows a parabolic path
until the object falls to the ground; see Figure below. If the object reaches a
maximum height (measured from the ground) of 7 m after traveling a horizontal
distance of 4 m, determine the horizontal distance between the object’s initial
and final positions.
7. The vertex of the parabola can be
A. (0,7)
B. (7,0)
A. (0,0)
B. (-4,2)

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40
40
For items 7-10, refer to the following scenario:
An object thrown from a height of 2 m above the ground follows a parabolic path
until the object falls to the ground; see Figure below. If the object reaches a
maximum height (measured from the ground) of 7 m after traveling a horizontal
distance of 4 m, determine the horizontal distance between the object’s initial
and final positions.
8. The equation of the parabola is
A. 𝑥2
= 4c(y-7)
B. 𝑥2
= -4c(y-7)
C. 𝑦2= 4c(x-7)
B. 𝑦2
= -4c(x-7)

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41
41
For items 7-10, refer to the following scenario:
An object thrown from a height of 2 m above the ground follows a parabolic path
until the object falls to the ground; see Figure below. If the object reaches a
maximum height (measured from the ground) of 7 m after traveling a horizontal
distance of 4 m, determine the horizontal distance between the object’s initial
and final positions.
9. The starting point of the object can
be viewed at which point?
A. (2, -4)
B. (-4, 2)
C. (-2, 4)
B. (4, -2)

42. Click to edit Master title style
42
42
For items 7-10, refer to the following scenario:
An object thrown from a height of 2 m above the ground follows a parabolic path
until the object falls to the ground; see Figure below. If the object reaches a
maximum height (measured from the ground) of 7 m after traveling a horizontal
distance of 4 m, determine the horizontal distance between the object’s initial
and final positions.
10. In the parabola, if the value of c=
4
5
,
which of the following could be the
equation of the parabola?
A. 𝑥2 = 16
5
(𝑦−7)
B. 𝑥2 = -16
5
(𝑦−7)
C. 𝑦2= 16
5
(𝑥−7)
B. 𝑦2= -16
5
(𝑥−7)

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43
For items 11-12, refer to the following scenario:
A tunnel has the shape of semi ellipse that is 15ft at the center, and 36ft across
at the base. At how high should a passing truck be, if it 12ft wide, for it to be
able to fit through the tunnel? Round off your answer to two decimal places.
11. If the center is at (0,0), then which
of the following could be the equation
of the ellipse?
A.
𝑥2
182 +
𝑦2
152 = 1
B.
𝑥2
152 +
𝑦2
182 = 1
C.
𝑥2
62 +
𝑦2
152 = 1
B.
𝑥2
152 +
𝑦2
62 = 1

44. Click to edit Master title style
44
44
For items 11-12, refer to the following scenario:
A tunnel has the shape of semi ellipse that is 15ft at the center, and 36ft across
at the base. At how high should a passing truck be, if it 12ft wide, for it to be
able to fit through the tunnel? Round off your answer to two decimal places.
12. From the problem, since the width of the
truck is 12ft, then which of the following is the
correct solution in finding the height of the
truck?
A. 𝑥2
182 + 𝑦2
152 = 1, so if x = 6, then 62
182 + 𝑦2
152 = 1, and thus y=10√2
B. 𝑥2
152 + 𝑌2
182 = 1, so if x = 6, then 62
152 + 𝑦2
152 = 1, and thus y=18√21
5
C. 𝑥2
62 + 𝑦2
152 = 1, so if x= 6, then 62
62 + 𝑦2
152 = 1, and thus y = 0
D. 𝑥2
152 + 𝑦2
6
= 1, so if x= 6, then 62
152 + 𝑦2
62 = 1, and thus y = 6√21
5
0

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45
45
For items 13-15, refer to the following scenario:
Two stations, located at M (-1.5, 0) and N (1.5, 0) (units are in km),
simultaneously send sound signals to a ship, with the signal traveling at the
speed of 0.33 km/s. if the signal from N was received by the ship four seconds
before the signal it received from M, find the equation of the curve containing
the possible location of the ship.
13. From the problem, how far in km are the two stations?
A. 1.50 B. 3.00 C. 1.32 D. 1.81

46. Click to edit Master title style
46
46
For items 13-15, refer to the following scenario:
Two stations, located at M (-1.5, 0) and N (1.5, 0) (units are in km),
simultaneously send sound signals to a ship, with the signal traveling at the
speed of 0.33 km/s. if the signal from N was received by the ship four seconds
before the signal it received from M, find the equation of the curve containing
the possible location of the ship.
14. How far is the ship from point M in km?
A. 1.50 B. 3.00 C. 1.32 D. 1.81

47. Click to edit Master title style
47
47
For items 13-15, refer to the following scenario:
Two stations, located at M (-1.5, 0) and N (1.5, 0) (units are in km),
simultaneously send sound signals to a ship, with the signal traveling at the
speed of 0.33 km/s. if the signal from N was received by the ship four seconds
before the signal it received from M, find the equation of the curve containing
the possible location of the ship.
15. Which of the following is the equation of the curve
containing the possible location of the ship?
A.
𝑥2
0.4356
-
𝑦2
1.8144
= 1 C.
𝑦2
0.4356
-
𝑥2
1.8144
= 1
B.
𝑥2
1.8144
-
𝑦2
0.5346
= 1 D.
𝑦2
1.8144
-
𝑥2
0.4356
= 1

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48
GREAT
JOB!