Analytic Geometry

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pre-cal 30s math : analytic geometry unit.

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Analytic Geometry

  1. 2. COORDINATE EQUATION PROBLEMS: PROCESS 1 EXAMPLES: a) Given the coordinate equation  7 = (x-5)² + (y+6)², change it to the form  0 = x² + y² + dx + ey + f . b) Given the coordinate equation  18 = (x+3)² + (y-4)², change it to the form  0 = x² + y² + dx + ey + f .
  2. 3. Solution to a) : Solution to b): PROCESS 1 SOLUTIONS:
  3. 4. PROCESS 2 EXAMPLES: c) Given the centre (-4,7), and the radius √26, write the coordinate equation. d) Given the centre (9,-2), and the radius √54, write the coordinate equation.
  4. 5. Solution to c) : Solution to d) : PROCESS 2 SOLUTIONS:
  5. 6. PROCESS 3 EXAMPLE: Given the centre (4,-9), and the point (10,-3), write the coordinate equation.
  6. 7. PROCESS 3 SOLUTION:
  7. 8. PROCESS 4 EXAMPLE: Given the centre (7,12), and the area 21  , write the coordinate equation.
  8. 9. PROCESS 4 SOLUTION:
  9. 10. PERPENDICULAR DISTANCE PROBLEMS: PROCESS 1 EXAMPLE: Given the point P(3,5) and the line 12x + 4y +3 = 0, find the perpendicular distance.
  10. 11. PROCESS 1 SOLUTION:
  11. 12. PROCESS 2 EXAMPLE: Given the point P(2,5) and the line 3x + 5y = 8, find the perpendicular distance.
  12. 13. PROCESS 2 SOLUTION:
  13. 14. PROCESS 3 EXAMPLE: Given the lines -4y + x + 9 = 0 and y - 5x = 12, find the perpendicular distance.
  14. 15. PROCESS 3 SOLUTION:
  15. 16. LINEAR EQUATION SYSTEM PROBLEM: Solve by Graphing Example: Given this system : Solve graphically.   y = x² y = 6 - x²
  16. 17. Solve by Graphing solution: y = x²    x | y   -1   1         --->         P(-1,1)   0   0         --->          P(0,0)   1  1         --->          P(1,1)   2   4         --->          P(2,4)   3   9         --->          P(3,9)   4   16       --->          P(4,16)   5   25       --->          P(5,25) 6   36       --->          P(6,36)
  17. 18. y = 6 - x² y = - x² + 6    x | y   -1   5         --->        P(-1,5)   0   6         --->        P(0,6)   1  5         --->        P(1,5)   2   2         --->       P(2,2)   3   -3        --->        P(3,-3)   4   -10      --->        P(4,-10)   5   -19      --->        P(5,-19) 6   -30      --->        P(6,30)
  18. 19. (-1¾, 3) (1¾, 3) The Solutions are (-1¾, 3) and (1¾, 3) .
  19. 20. Solve by Substitution Example: Given this system : Solve using substitution.     12x - 4y = 9    y + 4x = 18
  20. 21. Solve by Substitution solution:
  21. 22. Solve by Elimination Example: Given this system :   4x + y = 30    -2x + 2y = 10 Solve using elimination.  
  22. 23. Solve by Elimination solution:
  23. 24. BIBLIOGRAPHY: http://www.univie.ac.at/future.media/moe/fplotter/fplotter.html

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