PPT-Conic Sections Practice

Find the equation of the conic section using the given information Ellipse covertices and foci   Find the equation of the conic section using the given information Circle center 45 and tangent to the yaxis. 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 Eccentricity – . The ratio of distances. . It basically tells how close a conic section is to being a circle.. In a parabola: . . e. . = 1. In an ellipse or hyperbola:. The . ratio between the foci and the vertices. Michael Woltermann. Mathematics Department. Washington and Jefferson College. Washington, PA 15301-4801. Triumph der Mathematik. 100 Great Problems of Elementary Mathematics. By Heinrich D. 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).. 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.. 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 . What are Cross Sections?. Cross Sections are defined as the shape we get when cutting straight through an object. They can be determined by how the cross section flows…whether vertically or horizontally.. 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. , . PARABOLA. AND . HYPERBOLA. ARE CALLED CONIC SECTIONS. BECAUSE . THESE CURVES APPEAR ON THE SURFACE OF A CONE . WHEN IT IS CUT BY SOME TYPICAL CUTTING PLANES.. Section Plane. Through Generators. 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. 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.. TThheessiimmpplleeaannddccoonnvveenniieenncceepprreevveennttssccrraattcchheesssshheeeettNEWSDec 2014TEL81-868-38-6154 FAX81-868-38-6331E-mail toolsconiccojpURL http//wwwconiccojp/EnPage/indexhtmlEEaas July 28029,2016 Berlin, Germany. Exact analytical aberration theory . of centered optical systems . containing conic surfaces. Boian. . Andonov. . Hristov. , Prof. (. Ph.D. ) . Bulgarian Academy . of Sciences. 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.