PPT-Hyperbolas

Standard Form Transverse axis axis that vertices lie on Horizontal Center hk Slopes of asymptotes a comes first   Standard Form Transverse axis axis that vertices lie on Vertical . 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: , 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. = ± . By: Leonardo Ramirez. Pre Calculus. Per.6. Mr. Caballero. Hyperbola. What is a Hyperbola?. The term hyperbola was introduced by the Greek mathematician Apollonius of . Perga. as well as the terms Parabola, and Ellipse. . Definitions. . A. . hyperbola. . is the set of all point P such that the difference of the distances between P and two fixed points, called the . foci. , is a constant. . The. . transverse axis. . 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.. 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. The Ellipse. Basic oval. Has a center point, 2 foci, focal axis, and 2 vertices on the focal axis. https://. www.youtube.com/watch?v=7UD8hOs-vaI. The ellipse. The ellipse: formulas. Ellipses with center (0, 0). 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?