Ellipse Section 7.3.

Slides:

Advertisements

Similar presentations

10.4 Ellipses p An ellipse is a set of points such that the distance between that point and two fixed points called Foci remains constant d1 d2.

Advertisements

11.2 The Ellipse.

Section 11.6 – Conic Sections

Math 143 Section 7.1 The Ellipse

Chapter 9 Analytic Geometry.

Ellipses Objective: Be able to get the equation of an ellipse from given information or the graph Be able to find the key features of and graph an ellipse.

Ellipse Conic Sections.

Questions over Assignment  3R- One more thing we need to do on 8, 9, & 10.

Advanced Geometry Conic Sections Lesson 4

Chapter Hyperbolas.

Unit #4 Conics. An ellipse is the set of all points in a plane whose distances from two fixed points in the plane, the foci, is constant. Major Axis Minor.

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

Conic Sections - Hyperbolas

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.

Ax 2 + Bxy + Cy 2 + Dx + Ey + F=0 General Equation of a Conic Section:

Ellipses Part 1 Circle/Ellipse Quiz: March 9 Midterm: March 11.

Ellipses Topic 7.4. Definitions Ellipse: set of all points where the sum of the distances from the foci is constant Major Axis: axis on which the foci.

Ellipses Topic Definitions Ellipse: set of all points where the sum of the distances from the foci is constant Major Axis: axis on which the foci.

10.3 The Ellipse.

Warm up Write the standard form of the equation: Then find the radius and the coordinates of the center. Graph the equation.

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.

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.

Warm-Up Write the standard equation of the circle with the given radius and center. 1) 9; (0,0) 2) 1; (0,5) 3) 4; (-8,-1) 4) 5; (4,2)

8.4 Hyperbola 5/22/2013. Hyperbola Definition: is a conic section in which difference of distances of all the points from two fixed points (called `foci`)

Conic Sections The Ellipse Part A. Ellipse Another conic section formed by a plane intersecting a cone Ellipse formed when.

Definition: An ellipse is the set of all points in a plane such that the sum of the distances from P to two fixed points (F1 and F2) called foci is constant.

Lake Zurich High School

Accelerated Precalculus Ellipses. One Minute Question Find the diameter of: x 2 + y 2 + 6x - 14y + 9 = 0.

Conics Ellipses. Ellipse Definition: the set of all points in a plane whose distances from two fixed points in the plane have a constant sum. The fixed.

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.

Today’s Date: 2/5/ Ellipses.

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.

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

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.

Hyperbolas Objective: graph hyperbolas from standard form.

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

Ellipses Date: ____________.

Graph and Write Equations of Elllipses

Chapter 3 Conics 3.4 The Ellipse MATHPOWERTM 12, WESTERN EDITION

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

MATH 1330 Section 8.2b.

Ellipses & Hyperbolas.

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

Graph and Write Equations of Ellipses

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.

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

MATH 1330 Section 8.3.

O E L Y K x *Parent graph: center is at the origin *2 axes of symmetry *EY is the major axis and always contains the foci *KL is the minor axis.

Ellipse Conic Sections.

Conic Sections - Ellipses

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

Conic Sections The Ellipse Part A.

Ellipse Conic Sections.

Section 10.2 Ellipses.

Ellipse Last Updated: October 11, 2005.

MATH 1330 Section 8.3.

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

4 minutes Warm-Up Write the standard equation of the circle with the given radius and center. 1) 9; (0,0) 2) 1; (0,5) 3) 4; (-8,-1) 4) 5; (4,2)

THE ELLIPSE Week 17.

Section 11.6 – Conic Sections

5.3 Ellipse (part 2) Definition: An ellipse is the set of all points in a plane such that the sum of the distances from P to two fixed points (F1 and.

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).

Warm up: Write an equation for the circle that has center (5, 0), and radius 6 units. A. x2 + (y – 5)2 = 36 B. x2 – (y – 5)2 = 36 C. (x – 5)2 + y2 = 36.

Hyperbolas 12-4 Warm Up Lesson Presentation Lesson Quiz

Presentation transcript:

Ellipse Section 7.3

Definitions The ellipse with foci F1 and F2 is the set of all point M for which the sum of the distances to the foci is constant. There are two cases according to the major axis containing the foci.

What does it look like? B2(0,b) A2(0,a) M M F2(c,0) F1(-c,0) A2(a,0)

Observations For any point M on the ellipse we have: d(M,F1) + d(M,F2) = 2a The four vertices of the ellipse are A1, A2, B1 and B2 The major axis is the line segment A1A2 with length 2a The foci F1 and F2 are located on the major axis and the focal distance between them is 2c

Observations The minor axis is the line segment B1B2 with length 2b The axes of the ellipse are axes of symmetry The center O of the ellipse is the center of symmetry The parameters a, b and c form a Pythagoras Triangle a2 = b2 + c2 B2 a b NOTICE a is the hypotenuse!! c F2

How to Draw an Ellipse B2(0,3) F2(4,0) F1(-4,0) A2(5,0) Find a (bigger number) a = √25 = 5 Find b b = √9 = 3 Find c a2 = b2 + c2  a2 – b2 = c2 c2 = 25-9 c2 = 16 c = √16 = 4 B1(0,-3) Major Axis? x-axis Find vertices & Foci A1(-5,0), A2(0,-5) B1(0,-3), B2(0,3) F1(-4,0), F2(4,0)

How to Find the Rule 8 Major Axis? y-axis What do we have? a=8 and b=4 Find a2 and b2 a2=82=64 a2=42=16 Write Rule (we do not need c to write the rule!) 4

Example Major Axis? x-axis 2 What do we have? c=3 and b=2 Find a2 and b2 a2 = b2 + c2 a2 = 22 + 32 a2 = 13 b2 = 4 Write Rule 2 F2(3,0)

Homework Workbook p.332 #1,3,4 p. 333 #5,6,7