PPT-CONIC SECTIONS ELLIPSE

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. 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. Motions of the Planets. The ancient astronomers believed that the Universe was made up of spheres (orbs). The sphere that contained all of the objects seen in space was the Celestial Sphere. The sphere rotated around the earth making it appear as if all celestial objects were revolving around the earth. In this image you can see the stars and the Sun look as if they’re attached to the sphere Where is the person in the image trying to get to?. Solve each equation.. 1.. 27 = . x. 2. + 11 . 2.. . x. 2. = 48 . 3.. 84 = 120 – . x. 2. Ellipses - Warm Up. 1.. 27 = . x. 2. + 11. 16 = . x. 2. . x. = . ± 16 = ±4. BY Alec Marshak & Kyle Harding. Supplies. Two pushpins. A piece of computer paper. A big piece of cardboard. A 20cm long piece of string that is tied together to form a loop. Lastly you need a pencil. 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).. 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. 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. Properties of Circles . The circle is a frequently used component in pictures and graphs, a procedure for generating either full circles or circular arcs is included in most graphics packages.. A circle is defined as the set of points . TThheessiimmpplleeaannddccoonnvveenniieenncceepprreevveennttssccrraattcchheesssshheeeettNEWSDec 2014TEL81-868-38-6154 FAX81-868-38-6331E-mail toolsconiccojpURL http//wwwconiccojp/EnPage/indexhtmlEEaas 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.. An . ellipse. is the set of points in a plane for which the sum of the distances from two fixed points is a given constant. The two fixed points are the focal points of the ellipse; the line passing through the focal points is called the axis. The points of intersection of the axes and the ellipse are called the vertices..