PDF-CONIC SECTIONS - ELLIPSESExample 2:Find the coordinates of the center,

We know that the standard equations of the ellipse are as follows where horizontal major axisor where vertical major axisIn order to find the information asked for we must convert to st. 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: , Graphing these two points in a coordinate system allows us to recognize that this must be an ellipse with a horizontal major axis since the foci always lie on the major axis. , where NOTE: Graphing 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).. Conic sections will be defined in two different ways in this unit.. The set of points formed by the intersection of a plane and a double-napped cone.. The set of points satisfying certain conditions in relationship to a fixed point and a fixed line or to two fixed points. OTHER VIEW OF CONIC SECTIONS. 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.. 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 . Basic hyperbola vocab. Hyperbola. : Set of all points P such that the . difference. of the distance between P and two fixed points (foci) is a constant. Vertices. : The line through the foci intersects the hyperbola at the vertices. 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. 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.. 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.