PPT-Chapter 6: Conic Sections, Polar Coordinates and

Parametric Equations 6 1 Introduction The General Quadratic Equation in x and y has the form Where A B C D E F are constants The graphs of these equations are called Conic Sections. Example 2: Find the coordinates of the center, vertices, foci, and the equations of the asymptotes of the hyperbola given by . We know that the standard equations of the hyperbola are as follows: , Vectors in three space. Team 6:. Bhanu Kuncharam. Tony Rocha-. Valadez. Wei Lu. The position vector . R. from the origin of . Cartesian coordinate system. to the point (x(t), y(t), z(t)) is given by the expression. We know that the standard equations of the ellipse are as follows: , where (horizontal major axis)or , where (vertical major axis)In order to find the information asked for, we must convert to st Part I: Polar Coordinates. Objectives. Objectives: Know how to convert between polar and Cartesian coordinates and how to sketch functions in polar coordinates. Corresponding Sections in Simmons 16.1,16.2,16.3. MATH 1112. S. F. Ellermeyer. Rectangular vs. Polar Coordinates. Rectangular coordinates are the usual (. x,y. ) coordinates.. Polar coordinates are (r,. θ. ) coordinates – where . θ. is the directed angle measured in the usual way and r is the directed distance from the origin to the point in question. “Directed distance” means that we travel in the direction of the terminal side of . Spring 2010. Math . 2644. Ayona Chatterjee. Conic sections result from intersection a cone with a plane.. PARABOLAS. A parabolas is the set of points in a plane that are equidistant from a fixed point F (called the focus) and a fixed line (called the directrix).. Find the equation of the conic section using the given information. Ellipse: co-vertices . and foci .  . Find the equation of the conic section using the given . information.. Circle: center (-4,5) and tangent to the y-axis. 11.1 - An . Introduction. Conic Sections - Introduction. A conic is a shape generated by intersecting two lines at a point . (vertex) and . rotating one line . (generator) around . the other . (axis) while . Introduction. Polar coordinates are an alternative system to Cartesian coordinates. Some processes and equations involving the Cartesian system can become very complicated. You can simplify some of these by using Polar coordinates instead. Parabola: the collection of all points that are equidistant from a point(focus) and a line(. directrix. ). 1. Distance from A to focus:. Distance from B to focus:. Distance from C to focus:. 2. Vertex at. Polar coordinates are an alternative system to Cartesian coordinates. Some processes and equations involving the Cartesian system can become very complicated. You can simplify some of these by using Polar coordinates instead. Section 11.6 – Conic Sections. Parabola – set of points in a plane that are equidistant from a fixed point (. d(F, P). ) and a fixed line (. d (P, Q). ).. Focus - the fixed point of a parabola.. Directrix - the fixed line of a parabola.. Algebra 2. Chapter 9. This Slideshow was developed to accompany the textbook. Larson Algebra 2. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. THE CIRCLE. CONIC SECTION – THE CIRCLE. Equation for a Circle. Standard Form: x² + y² = r². You can determine the equation for a circle by using the distance formula then applying the standard form equation..