Advanced Precalculus Notes 9.4 The Hyperbola Hyperbola: The set of all points in a plane, the difference of whose distances from two distinct fixed points.

Slides:

Advertisements

Similar presentations

11.2 Hyperbolas Objectives: Define a hyperbola

Advertisements

Section 11.6 – Conic Sections

Section 9.2 The Hyperbola. Overview In Section 9.1 we discussed the ellipse, one of four conic sections. Now we continue onto the hyperbola, which in.

10.1 Conics and Calculus. Each conic section (or simply conic) can be described as the intersection of a plane and a double-napped cone. CircleParabolaEllipse.

Hyperbola – a set of points in a plane whose difference of the distances from two fixed points is a constant. Section 7.4 – The Hyperbola.

Table of Contents Hyperbola - Finding the Equation Horizontal AxisVertical Axis Recall that the equations for the hyperbola are given by...

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 11.4 The Hyperbola.

10.4 Hyperbolas JMerrill Definition A hyperbola is the set of all points in a plane, the difference of whose distances from two distinct fixed point.

10.5 Hyperbolas What you should learn: Goal1 Goal2 Graph and write equations of Hyperbolas. Identify the Vertices and Foci of the hyperbola Hyperbolas.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 Section 9.2 The Hyperbola.

11.4 Hyperbolas ©2001 by R. Villar All Rights Reserved.

10.3 Hyperbolas. Circle Ellipse Parabola Hyperbola Conic Sections See video!

Section 9-5 Hyperbolas. Objectives I can write equations for hyperbolas I can graph hyperbolas I can Complete the Square to obtain Standard Format of.

Definition: A hyperbola is the set of points P(x,y) in a plane such that the absolute value of the difference between the distances from P to two fixed.

Lesson 9.3 Hyperbolas.

Sullivan PreCalculus Section 9.4 The Hyperbola Objectives of this Section Find the Equation of a Hyperbola Graph Hyperbolas Discuss the Equation of a Hyperbola.

Definition A hyperbola is the set of all points such that the difference of the distance from two given points called foci is constant.

OHHS Pre-Calculus Mr. J. Focht. 8.3 Hyperbolas Geometry of a Hyperbola Translations of Hyperbolas Eccentricity 8.3.

HYPERBOLA. PARTS OF A HYPERBOLA center Focus 2 Focus 1 conjugate axis vertices The dashed lines are asymptotes for the graphs transverse axis.

Hyperbolas 9.3. Definition of a Hyperbola A hyperbola is the set of all points (x, y) in a plane, the difference of whose distances from two distinct.

Advanced Geometry Conic Sections Lesson 4

Chapter Hyperbolas.

9.5 Hyperbolas PART 1 Hyperbola/Parabola Quiz: Friday Conics Test: March 26.

Conic Sections - Hyperbolas

THE HYPERBOLA. A hyperbola is the collection of all points in the plane the difference of whose distances from two fixed points, called the foci, is a.

Review Day! Hyperbolas, Parabolas, and Conics. What conic is represented by this definition: The set of all points in a plane such that the difference.

Conics A conic section is a graph that results from the intersection of a plane and a double cone.

50 Miscellaneous Parabolas Hyperbolas Ellipses Circles

& & & Formulas.

Section 7.3 – The Ellipse Ellipse – a set of points in a plane whose distances from two fixed points is a constant.

What is a hyperbola? Do Now: Define the literary term hyperbole.

Precalculus Unit 5 Hyperbolas. A hyperbola is a set of points in a plane the difference of whose distances from two fixed points, called foci, is a constant.

Hyperbolas. Hyperbola: a set of all points (x, y) the difference of whose distances from two distinct fixed points (foci) is a positive constant. Similar.

What is it?. Definition: A hyperbola is the set of points P(x,y) in a plane such that the absolute value of the difference between the distances from.

Algebra II Section 8-5 Hyperbolas. Hyperbola The set of all points in a plane such that the absolute value of the difference of the distances from 2 fixed.

Hyperbola Definition: A hyperbola is a set of points in the plane such that the difference of the distances from two fixed points, called foci, is constant.

Precalculus Section 6.4 Find and graph equations of hyperbolas Geometric definition of a hyperbola: A hyperbola is the set of all points in a plane such.

The Hyperbola. x y Transverse axis Vertex Focus Center A hyperbola is the set of points in a plane the difference whose distances from two fixed points.

Hyperbolas Objective: graph hyperbolas from standard form.

Section 10.4 Last Updated: December 2, Hyperbola  The set of all points in a plane whose differences of the distances from two fixed points (foci)

9.3 Hyperbolas Hyperbola: set of all points such that the difference of the distances from any point to the foci is constant.

An Ellipse is the set of all points P in a plane such that the sum of the distances from P and two fixed points, called the foci, is constant. 1. Write.

Conics A conic section is a graph that results from the intersection of a plane and a double cone.

9.4 THE HYPERBOLA.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Hyperbola Objective: Be able to get the equation of a hyperbola from given information or the graph Be able to find the key features of and graph a hyperbola.

Conic Sections - Hyperbolas

10.3 The Hyperbola.

Section 10.2 – The Ellipse Ellipse – a set of points in a plane whose distances from two fixed points is a constant.

Ellipses Ellipse: set of all points in a plane such that the sum of the distances from two given points in a plane, called the foci, is constant. Sum.

distance out from center distance up/down from center

9.5A Graph Hyperbolas Algebra II.

Hyperbola Last Updated: March 11, 2008.

MATH 1330 Section 8.3.

MATH 1330 Section 8.3.

Transverse Axis Asymptotes of a Hyperbola

MATH 1330 Section 8.3.

Warm-up: show work on same paper as p.649

Hyperbola Last Updated: October 11, 2005 Jeff Bivin -- LZHS.

MATH 1330 Section 8.3.

Hyperbolas Chapter 8 Section 5.

10.5 Hyperbolas Algebra 2.

Section 11.6 – Conic Sections

5.4 Hyperbolas (part 2) Definition: A hyperbola is the set of points P(x,y) in a plane such that the absolute value of the difference between the distances.

Chapter 10 Conic Sections.

Applications of Trigonometric Functions

Presentation transcript:

Advanced Precalculus Notes 9.4 The Hyperbola Hyperbola: The set of all points in a plane, the difference of whose distances from two distinct fixed points (foci) is a constant. Transverse axis: line containing center and foci. Conjugate axis: line perpendicular to transverse axis, passing through the center.

Center: (h, k) Vertices: (h ± a, k)Vertices: (h, k ± a) Foci: (h ± c, k) Foci: (h, k ± c)

Graph the hyperbola: Label the center, vertices, foci and asymptotes. Center: Vertices: Foci: Asymptotes:

Find an equation of the hyperbola with center at the origin, one focus at (3, 0), and one vertex at (-2, 0).

Discuss the equation: Center: Vertices: Foci: Asymptotes:

Discuss the equation: Center: Vertices: Foci: Asymptotes:

Find an equation for the hyperbola with center at (1, -2), one focus at (4, -2), and one vertex at (3, -2).

Suppose that two people standing 1 mile apart both see a flash of lightning. After a period of time, the person standing at point A hears the thunder. One second later, the person standing at point B hears the thunder. If the person at B is due west of the person at A and the lightning strike is known to occur due north of the person standing at point A, where did the lighting strike?

Assignment: page 686: 1 – 17, 19, 25, 29, 35, 37, 39, 53, 54, 65