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1. Lesson 1.3 Graph and Properties of a Circle Precalculus Science, Technology, Engineering, and Mathematics

2. 2 The High Roller is the tallest Ferris wheel in the world. Notice that wherever you go, the shape of all Ferris wheels are circular. This allows them to carry more people and for easier rotation.

3. 3 In this lesson, we will learn how to plot or graph a circle on a rectangular coordinate system.

4. 4 How do we graph a circle on a Cartesian plane?

5. 5 Graph a circle in a rectangular coordinate system (STEM_PC11AG-Ia-4). Recognize the equation and important characteristics of a circle (STEM_PC11AG-Ie-1).

6. 6 Graph a circle on a rectangular coordinate system with center at the origin and center at . Graph a circle whose equation is written either in its standard form or the general form.  

7. 7 center at   Recall: Standard Form of the Equation of a Circle

8. 8 center at the origin   Recall: Standard Form of the Equation of a Circle

9. 9 In graphing a circle, we will use the standard form of the equation of a circle .   Graphing a Circle

10. 10 Steps in Graphing a Circle Step 1: Identify and plot the point on a coordinate plane.   Graphing a Circle  

11. 11 Steps in Graphing a Circle Step 2: Solve for   Graphing a Circle  

12. 12 Steps in Graphing a Circle Step 3: From the center count units horizontally in both directions, and vertically in both directions. This will give you four different points, all equidistant from the center.   Graphing a Circle          

13. Steps in Graphing a Circle Step 4: Connect these four points with the best curve that you can sketch to get the graph of the circle. Graphing a Circle          

14. Steps in Graphing a Circle Step 4: Connect these four points with the best curve that you can sketch to get the graph of the circle. Graphing a Circle          

15. Steps in Graphing a Circle Step 4: Connect these four points with the best curve that you can sketch to get the graph of the circle. Graphing a Circle          

16. Steps in Graphing a Circle Step 4: Connect these four points with the best curve that you can sketch to get the graph of the circle. Graphing a Circle    

17. If the given equation of a circle is in general form, transform the given equation into its equivalent standard form to identify the center and radius of the circle . Graphing a Circle

18. 18 How do you graph a circle given its equation in general form ?  

19. 19 Graph the equation .  

20. 20 Graph the equation .   The graph of the equation is shown on the right.  

21. 21 21 Graph the equation .  

22. 22 Graph the equation .  

23. 23 Graph the equation .   The graph of the equation is shown on the right.  

24. 24 24 Graph the equation .  

25. 25 Graph the equation .  

26. 26 Graph the equation .   The graph of the equation is shown on the right.  

27. 27 27 Graph the equation .  

28. 28 Graph the circle with center at and tangent to the 𝑦-axis.  

29. 29 Graph the circle with center at and tangent to the 𝑦-axis.   The graph of the circle with center at that is tangent to the -axis is shown on the right.  

30. 30 30 Graph the circle with center at and tangent to the 𝑥-axis.  

31. 31 Graph the circle with the given equation in standard form. 1. 2. 3.  

32. 32 Graph the circle with the given equation in general form. 1. 2. 3.  

33. 33 Steps in graphing a circle: 1. Identify and plot the point on a coordinate plane. 2. Solve for  

34. 34 Steps in graphing a circle: 3. From the center count units horizontally in both directions and vertically in both directions. This will give you four different points, all equidistant to the center.  

35. 35 Steps in graphing a circle: 4. Connect the points to form a circle by drawing a smooth curve. 5. Note that the center is not part of the graph of a circle.

36. 36 36 The area covered by the light of a bulb has a radius of 12 in. Considering the bulb as the origin on a coordinate plane and a moth on the point , will the moth die when the light is suddenly turned on? Explain your answer.  

37. 37 Slides 1 and 2: The High Roller at Night by Daniel Ramirez is licensed under CC BY 2.0 via Flickr .

38. 38 Barnett, Raymond, Michael Ziegler, Karl Byleen , and David Sobecki .  College Algebra with Trigonometry . Boston: McGraw Hill Higher Education, 2008. Bittinger , Marvin L., Judith A. Beecher, David J. Ellenbogen , and Judith A. Penna.  Algebra and Trigonometry: Graphs and Models . 4th ed. Boston: Pearson/Addison Wesley, 2009. Blitzer, Robert.  Algebra and Trigonometry . 3rd ed. Upper Saddle River, New Jersey: Pearson/Prentice Hal, 2007. Larson, Ron. Precalculus. 9th ed. Boston, MA: Cengage Learning, 2013. Stewart, James, Lothar Redlin, and Saleem Watson. Precalculus Mathematics for Calculus . 7th ed. Boston, MA: Cengage Learning, 2016.