Analytic Geometry
- 1. Ā
- 2. COORDINATE EQUATION PROBLEMS: PROCESS 1 EXAMPLES: a) Given the coordinate equationĀ 7 = (x-5)Ā² + (y+6)Ā², change itĀ to the form Ā 0 = xĀ² + yĀ² + dx + ey + f . b) Given the coordinate equationĀ 18 = (x+3)Ā² + (y-4)Ā², change itĀ to the form Ā 0 = xĀ² + yĀ² + dx + ey + f .
- 3. Solution to a) : Solution to b): PROCESS 1 SOLUTIONS:
- 4. PROCESS 2 EXAMPLES: c) Given theĀ centre (-4,7), and the radius ā26, write the coordinate equation. d) Given theĀ centre (9,-2), and the radius ā54, write the coordinate equation.
- 5. Solution to c) : Solution to d) : PROCESS 2 SOLUTIONS:
- 6. PROCESS 3 EXAMPLE: Given theĀ centre (4,-9), and theĀ point (10,-3), write the coordinate equation.
- 8. PROCESS 4 EXAMPLE: Given theĀ centre (7,12), and theĀ area 21 ļ° , write the coordinate equation.
- 10. PERPENDICULAR DISTANCE PROBLEMS: PROCESS 1 EXAMPLE: Given theĀ point P(3,5) and the line 12x + 4y +3 = 0, find the perpendicular distance.
- 12. PROCESS 2 EXAMPLE: Given theĀ point P(2,5) and the line 3x + 5y = 8, find the perpendicular distance.
- 14. PROCESS 3 EXAMPLE: Given the lines -4y + x + 9 = 0 and y - 5x = 12, find the perpendicular distance.
- 16. LINEAR EQUATION SYSTEM PROBLEM: Solve by Graphing Example: Given this system : Solve graphically.Ā Ā y = xĀ² y = 6 - xĀ²
- 17. Solve by Graphing solution: y = xĀ² Ā Ā x | yĀ Ā -1Ā Ā 1Ā Ā Ā Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā Ā Ā Ā P(-1,1) Ā Ā 0Ā Ā 0Ā Ā Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā Ā Ā Ā P(0,0) Ā Ā 1Ā 1Ā Ā Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā Ā Ā Ā P(1,1) Ā Ā 2Ā Ā 4Ā Ā Ā Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā Ā Ā Ā P(2,4) Ā 3Ā Ā 9Ā Ā Ā Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā Ā Ā Ā P(3,9) Ā 4Ā Ā 16Ā Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā Ā Ā Ā P(4,16) Ā 5Ā Ā 25Ā Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā Ā Ā Ā P(5,25) 6Ā Ā 36Ā Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā Ā Ā Ā P(6,36)
- 18. y = 6 - xĀ² y = - xĀ² + 6 Ā Ā x | yĀ Ā -1Ā Ā 5Ā Ā Ā Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā Ā Ā P(-1,5) Ā Ā 0Ā Ā 6Ā Ā Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā Ā Ā P(0,6) Ā Ā 1Ā 5Ā Ā Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā Ā Ā P(1,5) Ā Ā 2Ā Ā 2Ā Ā Ā Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā P(2,2) Ā 3Ā Ā -3Ā Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā Ā P(3,-3) Ā 4Ā Ā -10Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā Ā P(4,-10) Ā 5Ā Ā -19Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā Ā P(5,-19) 6Ā Ā -30Ā Ā Ā Ā Ā Ā --->Ā Ā Ā Ā Ā Ā Ā P(6,30)
- 19. (-1Ā¾, 3) (1Ā¾, 3) The Solutions are (-1Ā¾, 3) and (1Ā¾, 3) .
- 20. Solve by Substitution Example: Given this system : Solve using substitution.Ā Ā Ā 12x - 4y =Ā 9 Ā Ā y + 4x = 18
- 21. Solve by Substitution solution:
- 22. Solve by Elimination Example: Given this system : Ā 4x + y =Ā 30 Ā Ā -2xĀ + 2y = 10 Solve using elimination.Ā Ā
- 23. Solve by Elimination solution: