PPT-The Three Stooges, Conic Sections, Trigonometry, and Implicit Differentiation

Robert Davidson and Bob Gardner Department of Mathematics and Statistics East Tennessee State University Online at httpwwwetsuedumathgardnerstoogesStoogesTrig2012ppt. 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: , 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 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 . This is not a function, but it would still be nice to be able to find the slope.. Note use of chain rule.. This can’t be solved for . y. .. This technique is called implicit differentiation.. 1 Differentiate both sides w.r.t. . Section 3.7a. Consider the equation:. Is this a function?. Is the equation. differentiable?. If so, . how . do we. differentiate?. We use . implicit differentiation. , so named. b/c the functions are defined implicitly (hidden). 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. This is not a function, but it would still be nice to be able to find the slope.. Note use of chain rule.. This can’t be solved for . y. .. This technique is called implicit differentiation.. 1 Differentiate both sides w.r.t. . 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..