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# Analytical Geometry

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### Analytical Geometry

1. 1. ANGELS & DEMONS
2. 2. At the present time...
3. 3. Enclave within the City of Rome…
4. 4. …is the Vatican City where the papacy exists. But one tragic day, the unexpected occurred…
5. 5. The present pope suddenly passed away… mysteriously.
6. 6. The papal conclave was left with no choice but to convene to elect the new pontiff.
7. 7. These are the Cardinals who are considered to be the most likely candidates in the election
8. 8. UNFORTUNATELY
9. 9. the secret society of legend, long thought to be extinct, seems to have resurfaced
10. 10. 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
11. 11. 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...
12. 12. The lives of the four cardinals…
13. 13. VATICAN AND ITS PEOPLE…
14. 14. SAVE THEM AND THE WORLD FROM DESTRUCTION… CAN YOU?... . WILL YOU?....
15. 15. IT’S UP TO YOU
16. 16. You have to solve each problem correctly to proceed to the next location, find the next clue and solve the mystery.
17. 17. Each cathedral corresponds to an answer. You have to click the cathedral that corresponds to your answer.
18. 18. Let the quest begin!!!
19. 19. The path of light is laid, the sacred test, Let angels guide you on your lofty quest
20. 20. Where will the first crime happen?... To know, answer this…
21. 21. 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
22. 22. ELLIPSE
23. 23. 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.
24. 24. What is the perpendicular bisector of the major axis of an ellipse? X-axis Major axis Minor axis Y- axis View Answer
25. 25. MINOR AXIS
26. 26. WONDERFUL!!! YOU HAVE SAVED THE FIRST CARDINAL. NOW, YOU HAVE TO ANSWER CORRECTLY THIS PROBLEM IN ORDER TO GET TO THE NEXT LOCATION.
27. 27. 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
28. 28. x² + y²=1 a² b²
29. 29. 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.
30. 30. 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
31. 31. (x-h)²+(y-k)²=1 b² a²
32. 32. excellent!!! YOU HAVE SAVED THE second CARDINAL. NOW, YOU HAVE TO ANSWER CORRECTLY THIS PROBLEM IN ORDER TO GET TO THE NEXT LOCATION.
33. 33. 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
34. 34. 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
35. 35. 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.
36. 36. 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
37. 37. (h+a,k)=(3+5,-3) = (8,-3)
38. 38. WONDERFUL!!! YOU HAVE SAVED THE THIRD CARDINAL. NOW, YOU HAVE TO ANSWER CORRECTLY THIS PROBLEM IN ORDER TO GET TO THE NEXT LOCATION.
39. 39. 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
40. 40. 2a=2(5)=10 miles
41. 41. 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.
42. 42. 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
43. 43. (h,k-b)=(3,-3-4) =(3,-7)
44. 44. 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.
45. 45. 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
46. 46. (h,k+b)=(3,-3+4) =(3,1)
47. 47. 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.
48. 48. Who do you think is the culprit? This problem, when answered correctly, will reveal the mastermind.
49. 49. 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
50. 50. 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
51. 51. Congratulations!!! You have captured the real culprit… You have successfully finished the game.
52. 52. GAME OVER
53. 53. SUBMITTED AND CREATED BY: INTES, LUCILLE B. MALBAS, NIÑA LOVENDER H. NOLASCO, CECILLE MAE D. SUBMITTED TO: SIR VIE RYAN AMAMANGPANG