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

Slides:

Advertisements

Similar presentations

Section 11.6 – Conic Sections

Advertisements

10 – 5 Hyperbolas. Hyperbola Hyperbolas Has two smooth branches The turning point of each branch is the vertex Transverse Axis: segment connecting the.

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.

Table of Contents Ellipse - Finding the Equation Recall that the two equations for the ellipse are given by... Horizontal EllipseVertical Ellipse.

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.

10.5 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.

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

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.

SECTION: 10 – 3 HYPERBOLAS WARM-UP

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

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

Advanced Geometry Conic Sections Lesson 4

Chapter Hyperbolas.

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

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

& & & Formulas.

Translating Conic Sections

Write the standard equation for a hyperbola.

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.

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.

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.

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.

Fri 4/22 Lesson 10 – 6 Learning Objective: To translate conics Hw: Worksheet (Graphs)

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.

Conics 7.3: Hyperbolas Objectives:

Translating Conic Sections

6-3 Conic Sections: Ellipses

Ch 4: The Hyperbola Objectives:

Conic Sections - Hyperbolas

Vertices {image} , Foci {image} Vertices (0, 0), Foci {image}

Ellipses 5.3 (Chapter 10 – Conics). Ellipses 5.3 (Chapter 10 – Conics)

Chapter 9 Conic Sections.

Writing Equations of Conics

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.

Ellipses Objectives: Write the standard equation for an ellipse given sufficient information Given an equation of an ellipse, graph it and label the center,

9.4 Graph & Write Equations of Ellipses

MATH 1330 Section 8.3.

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

MATH 1330 Section 8.3.

Conic Sections: Hyperbolas

Warm-up Write the equation of an ellipse centered at (0,0) with major axis length of 10 and minor axis length Write equation of a hyperbola centered.

distance out from center distance up/down from center

Hyperbolas Chapter 8 Section 5.

Warm-Up Write the standard equation for an ellipse with foci at (-5,0) and (5,0) and with a major axis of 18. Sketch the graph.

Section 11.6 – Conic Sections

Chapter 10 Conic Sections.

Objective: Graphing hyperbolas centered at the origin.

Applications of Trigonometric Functions

Hyperbolas 12-4 Warm Up Lesson Presentation Lesson Quiz

The constant sum is 2a, the length of the Major Axis.

Chapter 7 Analyzing Conic Sections

Presentation transcript:

Hyperbolas 4.4 Chapter 10 – Conics

Yesterday’s Exit Slip Find the coordinates of the center of the graph. 1. 2. 3. 4. A. (–1, –1) B. (0, 0) C. (1, 0) D. (2, 1) Find the coordinates of the foci of the graph. A. (1, 1), (–1, 1) B. (2, 1), (–2, 1) C. (2, 0), (–2, 0) D. Find the length of the major axis of the graph. A. 8 B. 10 C. 12 D. 14 Find the length of the minor axis of the graph. A. 8 B. 6 C. 4 D. 2

Yesterday’s Exit Slip Graph the ellipse 5. A. B. C. D.

You graphed and analyzed equations of ellipses. (Lesson 10–4) Write equations of hyperbolas. Graph hyperbolas.

Hyperbolas

Graph of a Hyperbola hyperbola transverse axis conjugate axis foci vertices co-vertices constant difference

Writing the Equation of a Hyperbola Write an equation for the hyperbola shown. The center is the midpoint of the segment connecting the vertices, or (0, 0). The value of a is the distance from the center to a vertex, or 2 units. The value of c is the distance from the center to a focus, or 4 units. Find b: c2 = a2 + b2 The transverse axis is vertical → the y comes first when we write the equation 42 = 22 +b2 16 = 4 + b2 12 = b2

Example 1 What is an equation for the hyperbola? A. B. C. D.

Graphing Hyperbolas Identify the vertices, foci, and asymptotes. Step 1 Find the center. The center is at (3, –5). Step 2 Find a, b, and c. From the equation a2 = 4, so a = 2 and b2 = 9, so b = 3. c2 = a2 + b c2 = 4 + 9 c2 = 13 c = or about 3.61

Step 3 Identify the vertices and foci. The hyperbola is horizontal (x comes first in the equation) The vertices are 2 units from the center (given by knowing a) So the vertices are at (1, –5) and (5, –5). The foci are about 3.61 units from the center. The foci are at (6.61, –5) and (–0.61, –5). Step 4 Identify the asymptotes. Equation for the asymptote of a horizontal hyperbola a = 2, b = 3, h = 3, and k = –5 The equations for the asymptotes are

Step 5 Graph the hyperbola. Plot the points for the center, vertices, and foci Use the value for a and b to draw a box Graph the asymptotes by drawing in the diagonals of the box Draw symmetrical curves using the asymptotes as your guide

Example 2 Identify the asymptotes of the function A. B. C. D.