Warm up O Find the coordinates of the midpoint of the segment that has endpoints at (- 5, 4) and (7, - 2). O Find the distance between points at (10,

Slides:

Advertisements

Similar presentations

11.1 Intro to Conic Sections & The Circle. What is a “Conic Section”? A curve formed by the intersection of a plane and a double right circular cone.

Advertisements

Section 11.6 – Conic Sections

CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula.

Distance and Midpoint Formulas The distance d between the points (x 1, y 1 ) and (x 2, y 2 ) is given by the distance formula: The coordinates of the point.

Circles and Parabolas Review

Chapter 9 Analytic Geometry.

Introduction to Conic Sections

Introduction to Conic Sections

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

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.

50 Miscellaneous Parabolas Hyperbolas Ellipses Circles

Unit 1 – Conic Sections Section 1.2 – The Circle Calculator Required.

10.6 – Translating Conic Sections. Translating Conics means that we move them from the initial position with an origin at (0, 0) (the parent graph) to.

Section 2 Chapter Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives The Circle and the Ellipse Find an equation of a circle.

Jeopardy CirclesParabolasEllipsesHyperbolasVocabulary Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy Source:

Conic Sections Conic sections come from the double cones above and a plane that intersects one or both cones, the cross-section provided is then one of.

Copyright © 2011 Pearson Education, Inc. The Parabola Section 7.1 The Conic Sections.

Section 9.1 Quadratic Functions and Their Graphs.

Conics Conics Review. Graph It! Write the Equation?

Section 6.2 – The Circle. Write the standard form of each equation. Then graph the equation. center (0, 3) and radius 2 h = 0, k = 3, r = 2.

12.5 Circles in the Coordinate Plane

Conics Review Study Hard!. Name the Conic without graphing and write it in standard form X 2 + Y 2 -4Y-12=0.

Conic Sections.

Warm Up  What do you know about circles?. Algebra 3 Chapter 10: Quadratic Relations and Conic Sections Lesson 3: Circles.

We will only look at Circles and Parabolas this year.

MATH 1330 Section 8.2A. Circles & Conic Sections To form a conic section, we’ll take this double cone and slice it with a plane. When we do this, we’ll.

Find the distance between (-4, 2) and (6, -3). Find the midpoint of the segment connecting (3, -2) and (4, 5).

Unit 5: Conics Feb. 3, What is Conics? This is the short term for conic sections. -Conic Sections include circles, parabolas, ellipses, and hyperbolas.

GeometryGeometry Equations of Circles. GeometryGeometry Finding Equations of Circles You can write an equation of a circle in a coordinate plane if you.

Circles Ch10.3 and additional material. Geometric Definition: The intersection of a cone and a plane.

Distance The distance between any two points P and Q is written PQ. Find PQ if P is (9, 1) and Q is (2, -1)

Section 2.8 Distance and Midpoint Formulas; Circles.

Holt McDougal Geometry 12-7 Circles in the Coordinate Plane 12-7 Circles in the Coordinate Plane Holt Geometry Warm Up Warm Up Lesson Presentation Lesson.

Holt Geometry 11-7 Circles in the Coordinate Plane 11-7 Circles in the Coordinate Plane Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.

Equation of a Parabola. Do Now  What is the distance formula?  How do you measure the distance from a point to a line?

Chapter 10 – Conic Sections 1) Circles 2) Parabolas 3) Ellipses 4) Hyperbolas.

Copyright © 2011 Pearson Education, Inc. Conic Sections CHAPTER 13.1Parabolas and Circles 13.2Ellipses and Hyperbolas 13.3Nonlinear Systems of Equations.

10.0 Conic Sections. Conic Section – a curve formed by the intersection of a plane and a double cone. By changing the plane, you can create a circle,

WARM UP 13 (3/2, -5/2) Find the distance between the points 1. (8, 7) and (3, -5)2. (-5, 3) and (2, -7) Find the coordinates of the midpoints of the segments.

Chapter 10 Conic Sections

11.0 Analytic Geometry & Circles

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.

Analyzing Conic Sections

Warm Up circle hyperbola circle

Section 10.1 – The Circle.

Translating Conic Sections

Sections Conic Sections

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

Conic Sections Dr. Shildneck Fall, 2015.

Circles 4.1 (Chapter 10). Circles 4.1 (Chapter 10)

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

Conic Sections - Circles

Introduction to Conic Sections

9.3 Graph and Write Equations of Circles

Test Dates Thursday, January 4 Chapter 6 Team Test

Introduction to Conics: Parabolas

Chapter 9 Section 8: Equations of Circles.

28. Writing Equations of Circles

Analyzing Conic Sections

Section 11.6 – Conic Sections

What are Conic Sections?

Circles in the Coordinate Plane

10.1 Conics And 1.5 Circles Copyright © 2013 Pearson Education, Inc. All rights reserved.

10.6 – Translating Conic Sections

10.1 Conics And 1.5 Circles Copyright © 2013 Pearson Education, Inc. All rights reserved.

L10-2 Obj: Students will be able to find equations for parabolas

Chapter 7 Analyzing Conic Sections

Presentation transcript:

Warm up O Find the coordinates of the midpoint of the segment that has endpoints at (- 5, 4) and (7, - 2). O Find the distance between points at (10, 7) and (- 4, 8)

Lesson 10-2 Circles Objective: To use and determine the standard and general forms of the equation of a circle To graph circles

Conic Sections Formed when a plane intersects a double right cone.

Degenerate Conics O formed when the plane passes thru the vertex of the double right cone. degenerate ellipse degenerate hyperbola degenerate parabola

Circle O a set of points in a plane which are equidistant from a given point. (the center) O Radius – the distance from the center to any point on the circle.

Circle O The Standard Form of a circle with a center at (0,0) and a radius, r, is…….. O From Pythagorean Theorem center (0,0) radius = 2 Copyright © Oswego City School District Regents Exam Prep Center

Circles Now if the center moves off of the origin to point (h, k) we can use the distance formula to find the radius. (x, y) (h, k)

Circles O The Standard Form of a circle with a center at (h,k) and a radius, r, is…….. center (3,3) radius = 2 Copyright © Oswego City School District Regents Exam Prep Center

Example 1 O Write the standard form of the equation of the circle that is tangent to the x-axis and has its center at (-5, 4). Then graph the equation.

Example 2 O The equation of a circle is: Write the standard form of the equation. divide by 4 complete the square

Example 2 cont’d

Example 3 O Write the standard form of the equation of the circle that passes through the points at (1,1), (1, 2), and (2, 3). Then identify the center and radius of the circle. O Use the general equation O Use each point as x and y to create 3 new equations and solve the system for D, E and F. O Once found substitute D, E and F back into the original equation and complete the square (twice) to create the equation of the circle.