PPT-Ellipses & Hyperbolas

The Ellipse Basic oval Has a center point 2 foci focal axis and 2 vertices on the focal axis https wwwyoutubecomwatchv7UD8hOsvaI The ellipse The ellipse formulas Ellipses with center 0 0. Golub Rolf Strebel Dedicated to Ake Bj orck on the occasion of his 60 th birthday Abstract Fitting circles and ellipses to given points in the plane is a problem that arises in many application areas eg computer graphics 1 coordinate metrol ogy 2 pe edu EZRA BROWN Virginia Polytechnic Institute and State University Blacksburg VA 240610123 ezbrownmathvtedu After circles ellipses are probably the most familiar curves in all of mathematics Like circles they are a special subclass of the socalled co Short Answer Response. For each SAR, you will have a box like the one to the side that allows you ten (10) lines for your answer. You cannot write outside of the box, and you cannot “double line” in order to squeeze more writing in the box.. By: Amanda Anthony . Staci . Fetterman. Nicole Lloyd. Ashley Morgan. Definition. An ellipsis is a series of three points with spaces between them(. . .) inserted into a quotation to indicate the omission of material from the original quotation.. Hyperbola: a set of all points (x, y) the difference of whose distances from two distinct fixed points (. foci. ) is a positive constant. . Similar to ellipse, which is the SUM of distances. Every hyperbola has two disconnected branches. The line through the foci intersects a hyperbola at its two . Date: ______________. Horizontal. transverse axis:. 9.5 Hyperbolas. x. . 2. a. 2. y. 2. b. 2. –. = 1. y. x. V. 1. (–. a. , 0). V. 2. (. a. , 0). Hyperbolas with Center (0,0). asymptotes: . y. = ± . Standard Form:. Transverse axis (axis that vertices lie on): Horizontal . Center (. h,k. ). Slopes of asymptotes: . a comes first!.  . Standard Form:. Transverse axis (axis that vertices lie on): Vertical . Oh MY!. End Marks…AKA punctuation. PERIOD. Used at the end of a complete declarative sentence. Most sentences end with a period. It is also used after an abbreviation . Dr. Washington agreed with the diagnosis.. 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).. Graph hyperbolas by using the foci of a hyperbola. Hyperbolas. Result from slicing both cones in a double cone with one plane. Have 2 foci which determine the shape . Each branch opens away from the center.. 8. th. Writing. COMMA RULES!. Remember - commas save lives!. Let’s eat, Grandpa!. Let’s eat Grandpa!. 1. Between items in a series. A SERIES is a list of three or more words, phrases, or clauses.. This is it, the final grammar notes for the rest of the school year. . Dashes. Like commas, semicolons, colons, and ellipses, the dash represents an . interrupton. , or an abrupt change of thought. . 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 just an attempt to associate sums or differences of prime numbers with points lying on an ellipse or hyperbola.
Certain pairs of prime numbers can be represented as radius-distances from the focuses to points lying either on the ellipse or on the hyperbola.
The ellipse equation can be written in the following form: |p(k)| + |p(t)| = 2n.
The hyperbola equation can be written in the following form: ||p(k)| - |p(t)|| = 2n.
Here p(k) and p(t) are prime numbers (p(1) = 2, p(2) = 3, p(3) = 5, p(4) = 7,...),
k and t are indices of prime numbers,
2n is a given even number,
k, t, n ∈ N.
If we construct ellipses and hyperbolas based on the above, we get the following:
1) there are only 5 non-intersecting curves (for 2n=4; 2n=6; 2n=8; 2n=10; 2n=16). The remaining ellipses have intersection points.
2) there is only 1 non-intersecting hyperbola (for 2n=2) and 1 non-intersecting vertical line. The remaining hyperbolas have intersection points.
Will there be any new thoughts, ideas about this?