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.

Slides:

Advertisements

Similar presentations

10.1 Parabolas.

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.

Colleen Beaudoin February,  Review: The geometric definition relies on a cone and a plane intersecting it  Algebraic definition: a set of points.

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.

Hyperbolas and Rotation of Conics

Conic Sections Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Conic Sections Conic sections are plane figures formed.

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.

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

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

Lesson 9.3 Hyperbolas.

SECTION: 10 – 3 HYPERBOLAS WARM-UP

10.4 HYPERBOLAS. 2 Introduction The third type of conic is called a hyperbola. The definition of a hyperbola is similar to that of an ellipse. The difference.

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

Hyperbolas Section st Definiton A hyperbola is a conic section formed when a plane intersects both cones.

What is the standard form of a parabola who has a focus of ( 1,5) and a directrix of y=11.

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.

Warm up Find the equation in standard form of, Then give the coordinates of the center, the foci, and the vertices.

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

Conic Sections Advanced Geometry Conic Sections Lesson 2.

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

What am I?. x 2 + y 2 – 6x + 4y + 9 = 0 Circle.

MATT KWAK 10.2 THE CIRCLE AND THE ELLIPSE. CIRCLE Set of all points in a plane that are at a fixed distance from a fixed point(center) in the plane. With.

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.

10.5 Hyperbolas p.615 What are the parts of a hyperbola? What are the standard form equations of a hyperbola? How do you know which way it opens? Given.

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.

Making graphs and using equations of ellipses. An ellipse is the set of all points P in a plane such that the sum of the distance from P to 2 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)

Hyperbolas Date: ______________. Horizontal transverse axis: 9.5 Hyperbolas x 2x 2 a2a2 y2y2 b2b2 –= 1 y x V 1 (–a, 0)V 2 (a, 0) Hyperbolas with Center.

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

10.1 Conics and Calculus.

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.

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

9.4 THE HYPERBOLA.

6-3 Conic Sections: Ellipses

Ellipses Date: ____________.

Hyperbolas 4.4 Chapter 10 – Conics. Hyperbolas 4.4 Chapter 10 – Conics.

6-3 Conic Sections: Ellipses

MATH 1330 Section 8.2b.

Chapter 9 Conic Sections.

Ellipses & Hyperbolas.

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

31. Hyperbolas.

distance out from center distance up/down from center

9.5A Graph Hyperbolas Algebra II.

Hyperbola Last Updated: March 11, 2008.

WORKSHEET KEY 12/9/2018 8:46 PM 9.5: Hyperbolas.

MATH 1330 Section 8.3.

Transverse Axis Asymptotes of a Hyperbola

MATH 1330 Section 8.3.

31. Hyperbolas.

distance out from center distance up/down from center

10.5 Hyperbolas Algebra 2.

Section 11.6 – Conic Sections

Chapter 10 Conic Sections.

Presentation transcript:

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 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 vertices. This line connecting the vertices is called the transverse axis, the midpoint is the center.

Eccentricity: larger e (e>1) means flatter branches, close to 1 means more curve.

Standard Form of a Hyperbola VERTICAL HORIZONTAL

HORIZONTAL HYPERBOLAS

VERTICAL HYPERBOLAS

Find center, vertices, foci, and slope of asymptotes. Then graph.

Write in standard form. Find center, vertices, foci, and asymptotes. Then graph.

Write the equation of a hyperbola in standard form.

Identify as circle, ellipse, or hyperbola.