Section 10.3 – The Ellipse a > b a – semi-major axis

Slides:

Advertisements

Similar presentations

A circle is tangent to the x-axis at (-2, 0) and the y-axis at (0, 2). What is the equation of this circle?

Advertisements

Section 10.3 The Ellipse.

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

Section 7.3 The Ellipse. OBJECTIVE 1 Find an equation of the ellipse with center at the origin, one focus at (0, – 3) and a vertex at (5, 0). Graph.

Advanced Geometry Conic Sections Lesson 4

Ellipse Standard Equation Hyperbola. Writing equation of an Ellipse Example: write the standard form on an ellipse that has a vertex at (0,5) and co-vertex.

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.

Translating Conic Sections

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

Reflective properties of ellipse. Ellipse construction: w/id/ Demonstration with geogebra Major axis minor.

Sullivan Algebra and Trigonometry: Section 10.3 The Ellipse Objectives of this Section Find the Equation of an Ellipse Graph Ellipses Discuss the Equation.

a b Center at( h,k ) An ellipse with major axis parallel to x -axis c Definition.

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

Conics This presentation was written by Rebecca Hoffman.

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.

8.3 Ellipses May 15, Ellipse Definition: Is the set of all points such that the sum of the distances between the point and the foci is the same.

1 st Day Section A circle is a set of points in a plane that are a given distance (radius) from a given point (center). Standard Form: (x – h) 2.

Conic Sections Practice. Find the equation of the conic section using the given information.

Conics Name the vertex and the distance from the vertex to the focus of the equation (y+4) 2 = -16(x-1) Question:

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.

Get out Ellipse: Notes Worksheet and complete #2 & #3 (Notes Sheet From Yesterday)

Homework Log Wed 4/27 Lesson Rev Learning Objective:

6.2 Equations of Circles +9+4 Completing the square when a=1

PC 11.4 Translations & Rotations of Conics

Ellipses Date: ____________.

foci {image} None of these choices

Graph and Write Equations of Elllipses

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

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

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

MATH 1330 Section 8.2b.

Chapter 9 Conic Sections.

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.

Writing Equations of Conics

This presentation was written by Rebecca Hoffman

Review Circles: 1. Find the center and radius of the circle.

10.5 – The Conic Sections.

Today in Pre-Calculus Go over homework Chapter 8 – need a calculator

Find the focus of the parabola

ALGEBRA II HONORS/GIFTED - ELLIPSES

Warm-Up Range Graphically (#9 on CQ#1).

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

Unit 1 – Conic Sections Section 1.4 – The Ellipse Calculator Required

Test Dates Thursday, January 4 Chapter 6 Team Test

9.4 Graph & Write Equations of Ellipses

MATH 1330 Section 8.3.

Warm-Up Range Graphically (#9 on CQ#1).

Sullivan Algebra and Trigonometry: Section 11.3

MATH 1330 Section 8.3.

Ellipse Last Updated: October 11, 2005.

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

Writing Equations of Ellipses

Ellipse Skills Practice 70

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 10.3 The Ellipse Copyright © 2013 Pearson Education, Inc. All rights reserved.

Section 11.6 – Conic Sections

L10-4 Obj: Students will find equations for ellipses and graph ellipses. Ellipse Definition: Each fixed point F is a focus of an ellipse (plural: foci).

Graph information to Equation (going the other direction)

Jeopardy Solving for y Q $100 Q $100 Q $100 Q $100 Q $100 Q $200

Section 10.3 The Ellipse Copyright © 2013 Pearson Education, Inc. All rights reserved.

What is The equation of an Ellipse

Section 10.3 The Ellipse Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Presentation transcript:

Section 10.3 – The Ellipse a > b a – semi-major axis b – semi-minor axis C(h, k) V1(h + a, k), V2(h – a, k) F1(h + c, k), F2(h – c, k) C(h, k) V1(h, k + a), V2(h, k – a) F1(h, k + c), F2(h, k – c)

V1 V2 a F1 F2 c b C C(1, 4) V(1, -1), (1, 9) F(1, 0), (1, 8)

b c c V1 V2 a F1 F2 C C(-1, -2) V(-9, -2), (8, -2) F(-6.7, -2), (4.7, -2)

V1 V2 F1 F2 C C(0, 0) V(-4, 0), (4, 0) F(-2.6, 0), (2.6, 0)

Now graph it………

V1 V2 F1 F2 C C(-3, 1) V(-7, 1), (1, 1) F(-5, -1), (-1, 1)

Find the equation of the ellipse whose center is at (2, -2), vertex at (7, -2) and focus at (4, -2). C(2, -2) a = 5 c = 2 C F V

Find the equation of the ellipse with vertices at (4, 3) and (4, 9) , and focus at (4, 8) C(4, 6) a = 3 c = 2 V F C V

Find the equation of the ellipse whose foci are (5, 1) and (-1, 1), and length of the major axis is 8 C(2, 1) c = 3 Major is 8 Semi-major is 4 a = 4 F C F