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2.2 Parallel and Perpendicular Lines and Circles

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.

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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

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