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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. Solution X1=-2 Y1=-7

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

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

5. Practice Exercise

6. Answer to the Practice Exercise

7. 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.

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

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

10. Given line has slope –3/2.

11. Practice Exercise

12. Answers

13. 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.

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

15. Solution

16. Practice Exercises

17. Answers

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

19. Solution

20. Practice Exercise

21. Answer

22. The General Form of the Equation of a Circle

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

24. Solution

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

26. Practice Exercise

27. Answer

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