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ANGELS &
DEMONS
At the present
time...
Enclave within the
City of Rome…
…is the Vatican City
where the papacy
exists.

But one tragic day, the
unexpected occurred…
The present pope suddenly
passed away… mysteriously.
The papal conclave was left with no
choice but to convene to elect the
new pontiff.
These are the Cardinals who
are considered to be the most
likely candidates in the
election
UNFORTUNATELY
the secret society of legend, long thought
to be extinct, seems to have resurfaced
The four cardinals were held captives
and it was later revealed that the
Illuminati is the one responsible for it
and they have also stolen a canister
containing a quarter of a gram of
antimatter—an extremely dangerous
substance with immense destructive
potential comparable to a small nuclear
weapon, a potential unleashed upon
THE CARDINALS WILL BE KILLED ONE BY ONE IN
THEIR DESIGNATED CHURCH AND AFTER WHICH,
AS THE CLOCK STRIKES TWELVE, THE ANTIMATTER WILL EXPLODE AND DESTROY
EVERYTHING WITHIN ITS REACH...
The lives of the four
cardinals…
VATICAN AND ITS
PEOPLE…
SAVE THEM AND THE WORLD
FROM DESTRUCTION…

CAN YOU?... .
WILL YOU?....
IT’S UP TO YOU
You have to solve each problem correctly to
proceed to the next location, find the next
clue and solve the mystery.
Each cathedral corresponds to an answer.
You have to click the cathedral that
corresponds to your answer.
Let the quest begin!!!
The path of light is
laid, the sacred test,
Let angels guide you
on your lofty quest
Where will the first crime happen?...
To know, answer this…
It is the set of all points in the plane and
the sum of whose distances from two fixed
points is constant?

ellipse

conics

parabola

hyperbola

View Answer
ELLIPSE
GREAT!!! YOU HAVE UNVEILED
THE FIRST LOCATION. NOW, YOU
HAVE TO ANSWER CORRECTLY
THIS PROBLEM IN ORDER TO
SAVE THE FIRST CARDINAL AND
GET THE CLUE THAT WILL LEAD
YOU TO YOUR NEXT LOCATION.
What is the perpendicular bisector of the
major axis of an ellipse?

X-axis

Major axis

Minor axis

Y- axis
View Answer
MINOR AXIS
WONDERFUL!!! YOU HAVE
SAVED THE FIRST CARDINAL.
NOW, YOU HAVE TO ANSWER
CORRECTLY THIS PROBLEM IN
ORDER TO GET TO THE NEXT
LOCATION.
What is the standard form of the equation
of an ellipse which the foci on the x-axis
and center at the origin?

y=mx+b

x² + y²=1
a² b²

x² + y²=1
b² a²

ax²+bx+c=o

View Answer
x² + y²=1
a² b²
fantastic!!! YOU HAVE
UNVEILED THE second
LOCATION. NOW, YOU HAVE
TO ANSWER CORRECTLY
THIS PROBLEM IN ORDER
TO SAVE THE second
CARDINAL AND GET THE
next CLUE THAT WILL LEAD
YOU TO YOUR NEXT
LOCATION.
What is the standard form of the equation of
an ellipse with center at (h,k) and the foci
at (h,k+c) and (h,k-c)?

y²=x

(x-h)²+(y-k)²=1
b²
a²

(x-h)²+(y-k)²=1
a²
b²

y=x²
View Answer
(x-h)²+(y-k)²=1
b² a²
excellent!!! YOU HAVE
SAVED THE second
CARDINAL. NOW, YOU HAVE
TO ANSWER CORRECTLY THIS
PROBLEM IN ORDER TO GET
TO THE NEXT LOCATION.
Give the equation of the ellipse with foci at
(2,0) and (-2,0) and vertices at (4,0) and (4,0).

y=2x+12

x² + y²=1
36 25

x² + y²=1
16 12

16x²+12x+4=o

View Answer
e=c/a
=2/4
=1/2
b=√a² (1-e²)
= √16 (1-1/4)
= √16(3/4)
= √12
=2 √3
x² + y²=1
16 12
magnificent!!! YOU HAVE
UNVEILED THE third
LOCATION. NOW, YOU HAVE TO
ANSWER CORRECTLY THIS
PROBLEM IN ORDER TO SAVE
THE third CARDINAL AND GET
THE next CLUE THAT WILL
LEAD YOU TO YOUR NEXT
LOCATION.
Given: (x-3)²+(y+3)²=1
25

16

Find the exact location of Sta. Maria Della
Vittoria which is located east from the center.

(-2,-3)

(3,1)

(3,-7)

(8,-3)
View Answer
(h+a,k)=(3+5,-3)
= (8,-3)
WONDERFUL!!! YOU HAVE SAVED
THE THIRD CARDINAL. NOW,
YOU HAVE TO ANSWER
CORRECTLY THIS PROBLEM IN
ORDER TO GET TO THE NEXT
LOCATION.
Given: (x-3)²+(y+3)²=1
25
16
St . Peter’s Basilica is located West from the
center, based on the equation, find the
distance from the church where the cardinal
that represents the fire is held captive.

y=2x+12

x² + y²=1
36 25

x² + y²=1
16 12

16x²+12x+4=o

View Answer
2a=2(5)=10 miles
WOW!!! YOU HAVE UNVEILED
THE FOURTH LOCATION. NOW,
YOU HAVE TO ANSWER
CORRECTLY THIS PROBLEM IN
ORDER TO SAVE THE FOURTH
CARDINAL AND GET THE next
CLUE THAT WILL LEAD YOU TO
YOUR NEXT LOCATION.
Given: (x-3)²+(y+3)²=1
25

16

What is the exact location of Piazza Navona
from the center (3,-3)?

(3,-7)

(3,1)

(-2,-3)

(8,-3)
View Answer
(h,k-b)=(3,-3-4)
=(3,-7)
Good job!!! YOU HAVE SAVED
THE fourth CARDINAL.
NOW, YOU HAVE TO ANSWER
CORRECTLY THIS PROBLEM
IN ORDER TO deactivate
the anti-matter, to stop
it from exploding and
find out the lair of the
illuminati.
Given: (x-3)²+(y+3)²=1
25

16

What is the exact location of the Chigi
Chapel?

(3,-7)

(3,1)

(-2,-3)

(8,-3)

View Answer
(h,k+b)=(3,-3+4)
=(3,1)
TERRIFIC!!! YOU found the lair
of the illuminati, DEACTIVATED
THE ANTIMATTER, STOPPED IT
FROM EXPLODING AND SAVED THE
CARDINALS, VATICAN CITY AND
ITS PEOPLE AND MOST
ESPECIALLY, THE WORLD. ALL YOU
HAVE TO DO NOW IS CATCH THE
CULPRIT BEHIND ALL THESE.
Who do you think is the culprit?

This problem, when answered
correctly, will reveal the
mastermind.
Find the standard form of the equation of an
ellipse given the general equation
9x²+ y²+18x-12y-180=0

(x+1)²+(y-6)²=1
25
225

(x+1)²+(y-6)²=1
225
25
View answer
9x²+ y²+18x-12y-180=0
9x²+ 18x+y²-12y=180
9(x²+2x+1)+(y²-12y+36)=180+45
[9(x+1)² + (y-6)²=225]1/225
(x+1)² + (y-6)²=1
25
225
Congratulations!!!
You have captured
the real culprit…
You have
successfully
finished the game.
GAME
OVER
SUBMITTED AND CREATED BY:
INTES, LUCILLE B.
MALBAS, NIÑA LOVENDER H.
NOLASCO, CECILLE MAE D.
SUBMITTED TO:
SIR VIE RYAN AMAMANGPANG

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Analytical Geometry

  • 4. …is the Vatican City where the papacy exists. But one tragic day, the unexpected occurred…
  • 5. The present pope suddenly passed away… mysteriously.
  • 6. The papal conclave was left with no choice but to convene to elect the new pontiff.
  • 7. These are the Cardinals who are considered to be the most likely candidates in the election
  • 9. the secret society of legend, long thought to be extinct, seems to have resurfaced
  • 10.
  • 11. The four cardinals were held captives and it was later revealed that the Illuminati is the one responsible for it and they have also stolen a canister containing a quarter of a gram of antimatter—an extremely dangerous substance with immense destructive potential comparable to a small nuclear weapon, a potential unleashed upon
  • 12. THE CARDINALS WILL BE KILLED ONE BY ONE IN THEIR DESIGNATED CHURCH AND AFTER WHICH, AS THE CLOCK STRIKES TWELVE, THE ANTIMATTER WILL EXPLODE AND DESTROY EVERYTHING WITHIN ITS REACH...
  • 13. The lives of the four cardinals…
  • 14.
  • 16.
  • 17. SAVE THEM AND THE WORLD FROM DESTRUCTION… CAN YOU?... . WILL YOU?....
  • 19.
  • 20.
  • 21.
  • 22.
  • 23.
  • 24. You have to solve each problem correctly to proceed to the next location, find the next clue and solve the mystery.
  • 25. Each cathedral corresponds to an answer. You have to click the cathedral that corresponds to your answer.
  • 26. Let the quest begin!!!
  • 27. The path of light is laid, the sacred test, Let angels guide you on your lofty quest
  • 28.
  • 29.
  • 30. Where will the first crime happen?... To know, answer this…
  • 31. It is the set of all points in the plane and the sum of whose distances from two fixed points is constant? ellipse conics parabola hyperbola View Answer
  • 33. GREAT!!! YOU HAVE UNVEILED THE FIRST LOCATION. NOW, YOU HAVE TO ANSWER CORRECTLY THIS PROBLEM IN ORDER TO SAVE THE FIRST CARDINAL AND GET THE CLUE THAT WILL LEAD YOU TO YOUR NEXT LOCATION.
  • 34. What is the perpendicular bisector of the major axis of an ellipse? X-axis Major axis Minor axis Y- axis View Answer
  • 36. WONDERFUL!!! YOU HAVE SAVED THE FIRST CARDINAL. NOW, YOU HAVE TO ANSWER CORRECTLY THIS PROBLEM IN ORDER TO GET TO THE NEXT LOCATION.
  • 37. What is the standard form of the equation of an ellipse which the foci on the x-axis and center at the origin? y=mx+b x² + y²=1 a² b² x² + y²=1 b² a² ax²+bx+c=o View Answer
  • 39. fantastic!!! YOU HAVE UNVEILED THE second LOCATION. NOW, YOU HAVE TO ANSWER CORRECTLY THIS PROBLEM IN ORDER TO SAVE THE second CARDINAL AND GET THE next CLUE THAT WILL LEAD YOU TO YOUR NEXT LOCATION.
  • 40. What is the standard form of the equation of an ellipse with center at (h,k) and the foci at (h,k+c) and (h,k-c)? y²=x (x-h)²+(y-k)²=1 b² a² (x-h)²+(y-k)²=1 a² b² y=x² View Answer
  • 42. excellent!!! YOU HAVE SAVED THE second CARDINAL. NOW, YOU HAVE TO ANSWER CORRECTLY THIS PROBLEM IN ORDER TO GET TO THE NEXT LOCATION.
  • 43. Give the equation of the ellipse with foci at (2,0) and (-2,0) and vertices at (4,0) and (4,0). y=2x+12 x² + y²=1 36 25 x² + y²=1 16 12 16x²+12x+4=o View Answer
  • 44. e=c/a =2/4 =1/2 b=√a² (1-e²) = √16 (1-1/4) = √16(3/4) = √12 =2 √3 x² + y²=1 16 12
  • 45. magnificent!!! YOU HAVE UNVEILED THE third LOCATION. NOW, YOU HAVE TO ANSWER CORRECTLY THIS PROBLEM IN ORDER TO SAVE THE third CARDINAL AND GET THE next CLUE THAT WILL LEAD YOU TO YOUR NEXT LOCATION.
  • 46. Given: (x-3)²+(y+3)²=1 25 16 Find the exact location of Sta. Maria Della Vittoria which is located east from the center. (-2,-3) (3,1) (3,-7) (8,-3) View Answer
  • 48. WONDERFUL!!! YOU HAVE SAVED THE THIRD CARDINAL. NOW, YOU HAVE TO ANSWER CORRECTLY THIS PROBLEM IN ORDER TO GET TO THE NEXT LOCATION.
  • 49. Given: (x-3)²+(y+3)²=1 25 16 St . Peter’s Basilica is located West from the center, based on the equation, find the distance from the church where the cardinal that represents the fire is held captive. y=2x+12 x² + y²=1 36 25 x² + y²=1 16 12 16x²+12x+4=o View Answer
  • 51. WOW!!! YOU HAVE UNVEILED THE FOURTH LOCATION. NOW, YOU HAVE TO ANSWER CORRECTLY THIS PROBLEM IN ORDER TO SAVE THE FOURTH CARDINAL AND GET THE next CLUE THAT WILL LEAD YOU TO YOUR NEXT LOCATION.
  • 52. Given: (x-3)²+(y+3)²=1 25 16 What is the exact location of Piazza Navona from the center (3,-3)? (3,-7) (3,1) (-2,-3) (8,-3) View Answer
  • 54. Good job!!! YOU HAVE SAVED THE fourth CARDINAL. NOW, YOU HAVE TO ANSWER CORRECTLY THIS PROBLEM IN ORDER TO deactivate the anti-matter, to stop it from exploding and find out the lair of the illuminati.
  • 55. Given: (x-3)²+(y+3)²=1 25 16 What is the exact location of the Chigi Chapel? (3,-7) (3,1) (-2,-3) (8,-3) View Answer
  • 57. TERRIFIC!!! YOU found the lair of the illuminati, DEACTIVATED THE ANTIMATTER, STOPPED IT FROM EXPLODING AND SAVED THE CARDINALS, VATICAN CITY AND ITS PEOPLE AND MOST ESPECIALLY, THE WORLD. ALL YOU HAVE TO DO NOW IS CATCH THE CULPRIT BEHIND ALL THESE.
  • 58. Who do you think is the culprit? This problem, when answered correctly, will reveal the mastermind.
  • 59. Find the standard form of the equation of an ellipse given the general equation 9x²+ y²+18x-12y-180=0 (x+1)²+(y-6)²=1 25 225 (x+1)²+(y-6)²=1 225 25 View answer
  • 61. Congratulations!!! You have captured the real culprit… You have successfully finished the game.
  • 63.
  • 64. SUBMITTED AND CREATED BY: INTES, LUCILLE B. MALBAS, NIÑA LOVENDER H. NOLASCO, CECILLE MAE D. SUBMITTED TO: SIR VIE RYAN AMAMANGPANG