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2.2 Parallel and Perpendicular Lines and Circles PowerPoint Presentation
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2.2 Parallel and Perpendicular Lines and Circles

2.2 Parallel and Perpendicular Lines and Circles

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2.2 Parallel and Perpendicular Lines and Circles

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  1. 2.2 Parallel and Perpendicular Lines and Circles Slopes and Parallel Lines • If two nonvertical lines are parallel, then they have the same slopes. • If two distinct nonvertical lines have the same slope, then they are parallel. • Two distinct vertical lines, with undefined slopes, are parallel.

  2. Example 1: Writing Equation of a Line Parallel to a Given Line

  3. Solution X1=-2 Y1=-7

  4. What is the slope of the line? Given equation Slope of the line is –5.

  5. X1=-2, y1=-7, and m=-5

  6. Practice Exercise

  7. Answer to the Practice Exercise

  8. Slopes and Perpendicular Lines • If two nonvertical lines are perpendicular, then the product of their slopes is –1. • If the product of the slopes of two lines is –1, then lines are perpendicular. • A horizontal line having zero slope is perpendicular to a vertical line having undefined slope.

  9. Example 2: Finding the Slope of a Line Perpendicular to a

  10. Solution Solve the given equation for y. Slope is –3/2.

  11. Given line has slope –3/2.

  12. Practice Exercise

  13. Answers

  14. Definition of a Circle A circle is the set of all points in a plane that are equidistant from a fixed point called the center. The fixed distance from the circle’s center to any point on the circle is called the radius.

  15. The Standard Form of the Equation of a Circle Center Any point on the circle

  16. Example 3 Finding the Standard Form of a Circle’s Equation

  17. Solution

  18. Practice Exercises

  19. Answers

  20. Example 4: Using the Standard Form of a Circle’s

  21. Solution

  22. Practice Exercise

  23. Answer

  24. The General Form of the Equation of a Circle

  25. Example 5: Converting the General Form of Circle’s

  26. Solution

  27. r=2 h=-4 k=-2

  28. Practice Exercise

  29. Answer