March 27 th copyright2009merrydavidson. HYPERBOLA’S A hyperbola looks sort of like two mirrored parabolas.parabolas The two "halves" being called "branches".

Slides:

Advertisements

Similar presentations

Advertisements

C O N I C S E C T I O N S Part 4: Hyperbola.

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.

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.

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

10-4 Hyperbolas Warm Up Lesson Presentation Lesson Quiz Holt Algebra 2.

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.

Hyperbolas Topic 7.5.

10-4 Hyperbolas Warm Up Lesson Presentation Lesson Quiz Holt Algebra 2.

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

Hyperbolas. Standard Equation of a Hyperbol a (Horizontal Transverse Axis) Example: Slant asymptotes are at.

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 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.

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

Write the standard equation for a hyperbola.

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.

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.

Ellipse Notes. What is an ellipse? The set of all points, P, in a plane such that the sum of the distances between P and the foci is constant.

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.

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.

Hyperbolas or. Definition of a Hyperbola The hyperbola is a locus of points in a plane where the difference of the distances from 2 fixed points, called.

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.

Table of Contents Hyperbola - Definition and Equations Consider two fixed points in the plane, F 1 and F 2, which we shall call foci... Select a point.

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)

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.

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

March 22 nd copyright2009merrydavidson. Horizontal Ellipse An ellipse is the set of all points for which the sum of the distances at 2 fixed points is.

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.

6-3 Conic Sections: Ellipses

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.

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

Ch 4: The Hyperbola Objectives:

10.3 The Hyperbola.

Ellipses & Hyperbolas.

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

distance out from center distance up/down from center

Graph and Write Equations of Hyperbolas

9.5A Graph Hyperbolas Algebra II.

Hyperbola Last Updated: March 11, 2008.

Conic Sections: The Hyperbola

MATH 1330 Section 8.3.

Transverse Axis Asymptotes of a Hyperbola

10-4 Hyperbolas Warm Up Lesson Presentation Lesson Quiz Holt Algebra 2.

MATH 1330 Section 8.3.

10.5 Hyperbolas Algebra 2.

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.

Objective: Graphing hyperbolas centered at the origin.

Hyperbolas 12-4 Warm Up Lesson Presentation Lesson Quiz

Presentation transcript:

March 27 th copyright2009merrydavidson

HYPERBOLA’S A hyperbola looks sort of like two mirrored parabolas.parabolas The two "halves" being called "branches". A hyperbola has two foci and two vertices. Hyperbola’s also have asymptotes.

HYPERBOLA’S Definition: The set of all points for which the difference in the distance to two fixed points (called the foci) is constant.setpoints foci

Horizontal Hyperbola d2d2 d1d1 d 1 -d 2 = constant

Horizontal Hyperbola d2d2 d1d1 d 1 -d 2 = constant

Horizontal Hyperbola d2d2 d1d1 d 1 -d 2 = constant

Horizontal Hyperbola c = center to focus b = center to box a = center to vertex “x” term is positive

Major/Transverse axis goes through vertices. Minor/Conjugate axis a b c asymptote HORIZONTAL hyperbola

Vertical Hyperbola c = center to focus b = center to box a = center to vertex “y” term is positive

Major/Transverse axis goes through vertices. Minor/Conjugate axis b a c asymptote Vertical Hyperbola

Horizontal Hyperbola Vertical Hyperbola c 2 = a 2 + b 2 SUMMARY MAJOR axis does NOT mean longer.

Ex 1: Horizontal/Vertical?Center: a 2 =a= b 2 =b= c (-1,3) c 2 = a 2 + b 2 Let’s draw what we know so far…

Draw in the box. Ex 1: Draw in the asymptotes. Draw in the branches. Place “c” on the graph. F1: F2:

Ex 2: Horizontal/Vertical?Center: a 2 =a= b 2 =b=c = (0,1) c 2 = a 2 + b 2 Let’s draw what we know so far… Insert a “4” on your notes!

Draw in the box. Ex 2: Draw in the asymptotes. Draw in the branches. Place “c” on the graph. F1: F2:

Ex 3:Find the center, foci, and the equation of the asymptotes. Center: Major axis: horizontal or vertical a = Vertices b = c =Foci 4x 2 – y x - 4y -4 = 0 (2,-2) (4,-2),(0,-2)

Ex 4: Find the equation of the hyperbola if the vertices are at (5,0) and (-5,0) and b 2 = 49. Draw in what you know. Where is the vertex? (0,0) Major axis: H or V? Fill in the equation.

Ex 5. Write the equation for the hyperbola graphed on your notes.

HW: WS 10-5