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2. Using Boundless Presentations The Appendix The appendix is for you to use to add depth and breadth to your lectures. You can simply drag and drop slides from the appendix into the main presentation to make for a richer lecture experience. Free to edit, share, and copy Feel free to edit, share, and make as many copies of the Boundless presentations as you like. We encourage you to take these presentations and make them your own. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless Teaching Platform Boundless empowers educators to engage their students with affordable, customizable textbooks and intuitive teaching tools. The free Boundless Teaching Platform gives educators the ability to customize textbooks in more than 20 subjects that align to hundreds of popular titles. Get started by using high quality Boundless books, or make switching to our platform easier by building from Boundless content pre-organized to match the assigned textbook. This platform gives educators the tools they need to assign readings and assessments, monitor student activity, and lead their classes with pre-made teaching resources. Get started now at: If you have any questions or problems please email: educators@boundless.com http://boundless.com/teaching-platform

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4. Circles Ellipses Applications and Problem-Solving The Circle and the Ellipse Conic Sections > The Circle and the Ellipse Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra?campaign_content=book_196_section_50&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=dir ect&utm_source=boundless

5. The mathematical formula for a circle is (x–h)2+(y–k)2=r2, with the circle's center (h, k) and its radius, r. Circles Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/conic-sections-7/the-circle-and-the-ellipse-50/circles-216- 1930?campaign_content=book_196_section_50&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Circle terminology displayed View on Boundless.com Conic Sections > The Circle and the Ellipse

6. The length of a circumference of a circle can be found from the radius using the equation: [Equation 1]. Conic Sections > The Circle and the Ellipse Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/conic-sections-7/the-circle-and-the-ellipse-50/circles-216- 1930?campaign_content=book_196_section_50&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 1 View on Boundless.com

7. The area enclosed by a circle can be found from the radius using the formula: [Equation 2]. Conic Sections > The Circle and the Ellipse Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/conic-sections-7/the-circle-and-the-ellipse-50/circles-216- 1930?campaign_content=book_196_section_50&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 2 View on Boundless.com

8. An ellipse is like a stretched out circle, sometimes referred to as an oval. In mathematics, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. An ellipse is also the locus of all points of the plane whose distances to two fixed points (each called a focus) add to the same constant. Ellipses Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/conic-sections-7/the-circle-and-the-ellipse-50/ellipses-217- 5900?campaign_content=book_196_section_50&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess An ellipse as part of a cone View on Boundless.com Conic Sections > The Circle and the Ellipse

9. The formula for an ellipse is [Equation 3]. The area of an ellipse is given by [Equation 4], where a and b are one-half of the ellipse's major and minor axes respectively. Conic Sections > The Circle and the Ellipse Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/conic-sections-7/the-circle-and-the-ellipse-50/ellipses-217- 5900?campaign_content=book_196_section_50&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 3 View on Boundless.com Equation 4 View on Boundless.com

10. The equation for a circle is [Equation 5]. Where r=radius; (h,k)= center point coordinates. Applications and Problem-Solving Conic Sections > The Circle and the Ellipse Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/conic-sections-7/the-circle-and-the-ellipse-50/applications-and-problem- solving-218- 5895?campaign_content=book_196_section_50&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 5 View on Boundless.com

11. The equation for an ellipse is [Equation 6]. Where (h,k) = center point coordinates; a2 = major/minor axis length; b2 = major/minor axis length. Out of a and b, which ever value is greater, that will be the major axis. Applications and Problem-Solving Conic Sections > The Circle and the Ellipse Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/conic-sections-7/the-circle-and-the-ellipse-50/applications-and-problem- solving-218- 5895?campaign_content=book_196_section_50&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 6 View on Boundless.com

12. In order to determine the parameters of a circle or an ellipse, you must first put the equation into standard form as shown above. Applications and Problem-Solving Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/conic-sections-7/the-circle-and-the-ellipse-50/applications-and-problem- solving-218- 5895?campaign_content=book_196_section_50&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com Conic Sections > The Circle and the Ellipse

13. Free to share, print, make copies and changes. Get yours at www.boundless.com Appendix

14. Key terms circle A two-dimensional geometric figure, a line, consisting of the set of all those points in a plane that are equally distant from another point. ellipse A closed curve, the locus of a point such that the sum of the distances from that point to two other fixed points (called the foci of the ellipse) is constant; equivalently, the conic section that is the intersection of a cone with a plane that does not intersect the base of the cone. Free to share, print, make copies and changes. Get yours at www.boundless.com Conic Sections

15. Interactive Graph: A Circle Graph of a circle with the equation. In order to make a circle, both x and y terms must be squared. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph:." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-d8253ff8-ccd8-49e8-b1a1-122a28e91a97 View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-d8253ff8-ccd8-49e8-b1a1-122a28e91a97View on Boundless.com Conic Sections

16. Circle terminology Arc, sector, and segment. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Circle slices." Public domain http://en.wikipedia.org/wiki/File:Circle_slices.svg View on Boundless.comPublic domainhttp://en.wikipedia.org/wiki/File:Circle_slices.svgView on Boundless.com Conic Sections

17. Properties of an ellipse See text for descriptions of each element of this ellipse. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Ellipse Properties of Directrix and String Construction." Public domain http://en.wikipedia.org/wiki/File:Ellipse_Properties_of_Directrix_and_String_Construction.svg View on Boundless.comPublic domain http://en.wikipedia.org/wiki/File:Ellipse_Properties_of_Directrix_and_String_Construction.svgView on Boundless.com Conic Sections

18. Circle terminology displayed Chord, secant, tangent, radius, and diameter. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "CIRCLE LINES." CC BY-SA http://en.wikipedia.org/wiki/File:CIRCLE_LINES.svg View on Boundless.comCC BY-SAhttp://en.wikipedia.org/wiki/File:CIRCLE_LINES.svgView on Boundless.com Conic Sections

19. Interactive Graph: Graph of an Ellipse Graph of an ellipse with the equation Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph:." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-c0b4dec4-1c1e-488e-b360-98f4076363f6 View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-c0b4dec4-1c1e-488e-b360-98f4076363f6View on Boundless.com Conic Sections

20. A Circle A circle is defined as all the points that are a certain distance on a place from another point, the center. Free to share, print, make copies and changes. Get yours at www.boundless.com Connexions. "Circles." CC BY 3.0 http://cnx.org/content/m18245/latest/?collection=col10624/latest View on Boundless.comCC BY 3.0http://cnx.org/content/m18245/latest/?collection=col10624/latestView on Boundless.com Conic Sections

21. Voyager Path Using Gravity Assists The trajectories that enabled NASA's twin Voyager spacecraft to tour the four gas giant planets and achieve velocity to escape our solar system Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Orbital maneuver." Public domain http://en.wikipedia.org/wiki/Orbital_maneuver View on Boundless.comPublic domainhttp://en.wikipedia.org/wiki/Orbital_maneuverView on Boundless.com Conic Sections

22. An ellipse as part of a cone One definition of an ellipse is the intersection of a cone with an inclined plane. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Conicas1." CC BY-SA http://en.wikipedia.org/wiki/File:Conicas1.PNG View on Boundless.comCC BY-SAhttp://en.wikipedia.org/wiki/File:Conicas1.PNGView on Boundless.com Conic Sections

23. Free to share, print, make copies and changes. Get yours at www.boundless.com Conic Sections Find the area of a circle with a diameter of 8 inches. A) 8π in2 B) 4π in2 C) 16π in2 D) 64π in2

24. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Conic Sections Find the area of a circle with a diameter of 8 inches. A) 8π in2 B) 4π in2 C) 16π in2 D) 64π in2

25. Free to share, print, make copies and changes. Get yours at www.boundless.com Conic Sections What is the radius of the circle (x-1)2+(y+7)2=_______0? A) 7 B) 10 C) 1 D) 100

26. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Conic Sections What is the radius of the circle (x-1)2+(y+7)2=_______0? A) 7 B) 10 C) 1 D) 100

27. Free to share, print, make copies and changes. Get yours at www.boundless.com Conic Sections Find the circumference of a circle with a radius of 3 cm. A) 3π cm B) 9π cm C) 6π cm D) 36π cm

28. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Conic Sections Find the circumference of a circle with a radius of 3 cm. A) 3π cm B) 9π cm C) 6π cm D) 36π cm

29. Free to share, print, make copies and changes. Get yours at www.boundless.com Conic Sections What is the center of the circle (x-3)2+(y+4)2=49? A) (3,4) B) (3,-4) C) (-3,4) D) (7,7)

30. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Conic Sections What is the center of the circle (x-3)2+(y+4)2=49? A) (3,4) B) (3,-4) C) (-3,4) D) (7,7)

31. Free to share, print, make copies and changes. Get yours at www.boundless.com Conic Sections If the length of the major axis is 8 and the eccentricity of the ellipse is 0.625, what is the distance between the two foci? A) 4 B) 5 C) 12.8 D) 6

32. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Conic Sections If the length of the major axis is 8 and the eccentricity of the ellipse is 0.625, what is the distance between the two foci? A) 4 B) 5 C) 12.8 D) 6

33. Free to share, print, make copies and changes. Get yours at www.boundless.com Conic Sections Which of the following statements is NOT true about an ellipse? A) An ellipse has two foci that are equidistant from the center point. B) An ellipse is a special type of circle. C) The eccentricity of an ellipse is between 0 and 1. D) An ellipse has two axes of different lengths.

34. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Conic Sections Which of the following statements is NOT true about an ellipse? A) An ellipse has two foci that are equidistant from the center point. B) An ellipse is a special type of circle. C) The eccentricity of an ellipse is between 0 and 1. D) An ellipse has two axes of different lengths.

35. Free to share, print, make copies and changes. Get yours at www.boundless.com Conic Sections What is the area of the ellipse x2/36+y2/16=1? A) 36π B) 16π C) 30π D) 24π

36. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Conic Sections What is the area of the ellipse x2/36+y2/16=1? A) 36π B) 16π C) 30π D) 24π

37. Free to share, print, make copies and changes. Get yours at www.boundless.com Conic Sections You travel 50 ft on a bike, and the realize the wheel has spun around exactly 10 times. What is the radius of you wheel (to the nearest hundredth of a foot)? A) 1.59 ft B) 0.80 ft C) 5.00 ft D) 2.54 ft

38. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Conic Sections You travel 50 ft on a bike, and the realize the wheel has spun around exactly 10 times. What is the radius of you wheel (to the nearest hundredth of a foot)? A) 1.59 ft B) 0.80 ft C) 5.00 ft D) 2.54 ft

39. Attribution Connexions. "Circles." CC BY 3.0 http://cnx.org/content/m18245/latest/?collection=col10624/latestCC BY 3.0http://cnx.org/content/m18245/latest/?collection=col10624/latest Wiktionary. "circle." CC BY-SA 3.0 http://en.wiktionary.org/wiki/circleCC BY-SA 3.0http://en.wiktionary.org/wiki/circle Wikipedia. "Circle." CC BY-SA 3.0 http://en.wikipedia.org/wiki/CircleCC BY-SA 3.0http://en.wikipedia.org/wiki/Circle Connexions. "Conics Homework -- Homework: Ellipses." CC BY 3.0 http://cnx.org/content/m19088/latest/CC BY 3.0http://cnx.org/content/m19088/latest/ Connexions. "Conics Homework -- Homework: Circles." CC BY 3.0 http://cnx.org/content/m19084/latest/CC BY 3.0http://cnx.org/content/m19084/latest/ Wiktionary. "ellipse." CC BY-SA 3.0 http://en.wiktionary.org/wiki/ellipseCC BY-SA 3.0http://en.wiktionary.org/wiki/ellipse Wiktionary. "circle." CC BY-SA 3.0 http://en.wiktionary.org/wiki/circleCC BY-SA 3.0http://en.wiktionary.org/wiki/circle Connexions. "Ellipses." CC BY 3.0 http://cnx.org/content/m18247/latest/?collection=col10624/latestCC BY 3.0http://cnx.org/content/m18247/latest/?collection=col10624/latest Wiktionary. "ellipse." CC BY-SA 3.0 http://en.wiktionary.org/wiki/ellipseCC BY-SA 3.0http://en.wiktionary.org/wiki/ellipse Wikipedia. "Ellipse." CC BY-SA 3.0 http://en.wikipedia.org/wiki/EllipseCC BY-SA 3.0http://en.wikipedia.org/wiki/Ellipse Free to share, print, make copies and changes. Get yours at www.boundless.com Conic Sections