How do I determine the center and radius given an equation of a circle? How do quadratic relations model problems and their solutions? Objective(s): Students will: Verify theorems from basic geometry involving the distance between two points Verify that points (x, y) are an equal distance from a given point and a given line Use the defining characteristics of a conic section to find its equation Domain: Conic Sections 10.2 The Circle and The Ellipse (Coburn) Enduring Understanding(s): Vocabulary 10.1 The Ellipse (Blitzer) Cluster: Understand the properties of conic Ellipse, foci (focus), center, radius, vertices Ellipses arise from a locus of points that sections and apply them to model real-world (vertex), major axis, minor axis, standard form represent a constant sum of distances phenomena.* Additional Resource(s) of the equation of a circle, standard form of from two fixed points (foci). the equation of an ellipse Different forms of equations provide 2. From an equation in standard form, graph different information about key the appropriate conic section: ellipses, Algebra & Trigonometry (Coburn), 2nd Edition characteristics of the conic sections. Writing in Math/Discussion hyperbolas, circles, and parabolas. (Exercise Videos, Lecture Videos, Write an equation of the graph of a circle in Demonstrate an understanding of the Graphing Calculator Videos, standard form and describe how to graph it. Essential Question(s): relationship between their standard algebraic PowerPoint Presentations) form and the graphical characteristics. What information can be gathered from the equation of a circle or ellipse? 3. Transform equations of conic sections to Write an equation of the graph of an ellipse in convert between general and standard form. standard form and describe how to graph it. How do I determine the center and radius given an equation of a circle? Task(s) Determine whether the following statements How can ellipses be defined in relation to their foci? make sense or does not make sense and Circles, p. 11 explain your reasoning. How can I use the equation of a circle to Is It Really an Ellipse?, p. 39 I graphed an ellipse with a horizontal determine if a point lies on the graph?
How do I determine the center and radius given an equation of a circle? How do quadratic relations model problems and their solutions? Objective(s): Students will: Verify theorems from basic geometry involving the distance between two points Verify that points (x, y) are an equal distance from a given point and a given line Use the defining characteristics of a conic section to find its equation Domain: Conic Sections Cluster: Understand the properties of conic sections and apply them to model real-world phenomena.* 2. From an equation in standard form, graph the appropriate conic section: ellipses, hyperbolas, circles, and parabolas. Demonstrate an understanding of the relationship between their standard algebraic form and the graphical characteristics. 3. Transform equations of conic sections to convert between general and standard form. Enduring Understanding(s): Ellipses arise from a locus of points that represent a constant sum of distances from two fixed points (foci). Different forms of equations provide different information about key characteristics of the conic sections. Essential Question(s): What information can be gathered from the equation of a circle or ellipse? How do I determine the center and radius given an equation of a circle? How can ellipses be defined in relation to their foci? How can I use the equation of a circle to determine if a point lies on the graph? 10.2 The Circle and The Ellipse (Coburn) 10.1 The Ellipse (Blitzer) Additional Resource(s) Algebra & Trigonometry (Coburn), 2nd Edition (Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations) Task(s) Circles, p. 11 Is It Really an Ellipse?, p. 39 Vocabulary Ellipse, foci (focus), center, radius, vertices (vertex), major axis, minor axis, standard form of the equation of a circle, standard form of the equation of an ellipse Writing in Math/Discussion Write an equation of the graph of a circle in standard form and describe how to graph it. Write an equation of the graph of an ellipse in standard form and describe how to graph it. Determine whether the following statements make sense or does not make sense and explain your reasoning. I graphed an ellipse with a horizontal
Adv%20Alg%20_%20Trig%20Q4%20%2016-17%20Revised%2012-12-16.docx