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. Parentheses, Brackets. , . and . Ellipses. . Angela Gulick. CAS Writing Specialist. June . 2015. Parentheses. ( ) ( ) ( ) ( ) ( ) ( ) ( ). Use parentheses to enclose information that is interesting but not crucial. In other words, information in parentheses could be removed and you would still have a complete grammatical sentence. Parentheses should be used sparingly in college writing because they tend to produce a choppy effect. . Academic Essays. Green Hope Honor Code. Cheating: Numerous behaviors will be considered cheating. Some of these areas include, but are not limited to, the following: using cheat sheets; using former students’ notebooks; using internet resources without citing them as appropriate sources; misrepresenting something as being real and actual; using cell phones to create images of tests, quizzes, and/or other assignments; and text messaging with other students regarding a test or quiz. The use of technology in cheating can occur on small assignments such as homework assignments as well as on more formal tests, essays, and projects. Students can be guilty of cheating if they give out or are in receipt of the material.. Date: ____________. Ellipses. Standard Equation of an Ellipse. Center at (0,0). x. 2. a. 2. y. 2. b. 2. +. = 1. y. x. (–. a. , 0). . (. a. , 0). . (0, . b. ). (0, –. b. ). O. Horizontal Major Axis. A UWF Writing Lab Mini . Lesson. Mini-Lesson #63. DEFINITION. ELLIPSIS: a . punctuation mark . of three spaced dots (. . .) used to show an omission in writing or printing (Plural: . ellipses. ). Uses of Ellipses. 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. = ± . 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.. 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.. THE . DASH -. The dash (–) is used to set off additional material within a . sentence. Dashes are often used to . emphasize. the material they set off. . To . set off appositives that contain . commas. 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. Objective. You will be able to differentiate between Horizontal and Vertical Ellipses and then be able to sketch a graphical representation of the equation.. Vocabulary. Ellipse. : . the set of all points in a plane such that the . 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? Ellipses: . a punctuation mark of three spaced dots . (. . . .) used to show an omission in writing or printing (Plural: ellipses. ).. Uses of Ellipses. Use ellipses to show omitted material from a quoted passage in order to be fair to the author quoted and to maintain good grammar in the writer’s own work. Your resulting passage should be grammatically complete and correct..