Symmetry Every line through center

Slides:

Advertisements

Similar presentations

10-1 Exploring Conic Sections

Advertisements

Intro to Conic Sections. It all depends on how you slice it! Start with a cone:

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.

INTRO TO CONIC SECTIONS. IT ALL DEPENDS ON HOW YOU SLICE IT! Start with a cone:

Colleen Beaudoin February,  Review: The geometric definition relies on a cone and a plane intersecting it  Algebraic definition: a set of points.

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.

Circles – An Introduction SPI Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the.

GRAPHING QUADRATIC FUNCTIONS

Conic Sections By: Danielle Hayman Mrs. Guest Per. 4.

Section 9.1 Quadratic Functions and Their Graphs.

An Introduction to Conics

Conic Sections The Parabola. Introduction Consider a ___________ being intersected with a __________.

Center: (h, k) AOS: x = h and y = k Orientation: Horizontal if a >b Vertical if a

6-2 Conic Sections: Circles Geometric definition: A circle is formed by cutting a circular cone with a plane perpendicular to the symmetry axis of the.

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

Equations of Circles. You can write an equation of a circle in a coordinate plane, if you know: Its radius The coordinates of its center.

Polar Equations of Conics. Directrix is perpendicular to the polar axis at a distance p units to the left of the pole Directrix is perpendicular to the.

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)

Circle-Radius form By definition, a circle is the set of all points in a plane that lie a given distance from a given point. The given distance.

Friday, October 16 Write in vertex form by completing the square. 1) y = x 2 + 8x + 3 2) y = x x + 11.

Duration: 9 hours Subtopic: 1.1 Introduction to Conic Sections 1.2 Circles 1.3 Parabolas 1.4 Ellipses 1.5 Hyperbolas 1.6 The Intersection of Straight Line.

LESSON : CIRCLES. Circles: Circles have the form ( x – h)² + ( y – k)² = r² ( h,k) represents the center of the circle r represents the radius of the.

+ Equation of a Circle. + Circle A Circle is a set of all points in a plane equidistant from a given point. The Center.

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,

Equations of Circles.

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

CHAPTER 10 CONIC SECTIONS Section 1 - Circles

10.1 Circles and Parabolas Conic Sections

Equations of Circles.

Warm Up circle hyperbola circle

Asymptotes are drawn thru the box corners

6-3 Conic Sections: Ellipses

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

Conic Sections Anyway you slice it.

10.6 Equations of Circles Geometry.

Equations of Circles.

Introduction to Conic Sections

6-2 Conic Sections: Circles

Equations of Circles Part a.

(x2,y2) (3,2) (x1,y1) (-4,-2).

Conic Sections Dr. Shildneck Fall, 2015.

Conic Sections:Circles

Chapter 9 Conic Sections.

Writing Equations of Conics

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

Conic Sections - Circles

Equation of a Circle.

11.7 Circles in the Coordinate Plane

Equations of Circles.

Chapter 6: Analytic Geometry

4.1 Equations of circles Arcs, Inscribed Angles, Central Angles

Chapter 9 Section 8: Equations of Circles.

Objectives Write equations and graph circles in the coordinate plane.

The equation of a circle is based on the Distance Formula and the fact that all points on a circle are equidistant from the center.

Objectives and Student Expectations

Learning Target #21 Equations of Circles.

What are Conic Sections?

Intro to Conic Sections

Circles in the Coordinate Plane

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

Owen Skrelunas and Christian Morell

Objective: To write an equation of a circle.

Equations of Circles Advanced Geometry.

Center, Radius Form (x-h) + (y-k) = r (h,k) = Center r = radius

Center, Radius Form (x-h) + (y-k) = r (h,k) = Center r = radius

10.7 Write and Graph Equations of ⊙s

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

Chapter Equations of Circles.

Presentation transcript:

Symmetry Every line through center Ex 1) Write the equation given the center at (0,4) and a radius of 3. Center: (h,k) Radius: r Symmetry Every line through center Cone cut by a plane parallel to the base Real World: tunnels (h,k) r

Circles Steps to graph Steps to write equation Find center Find radius Plot center Count left, right, up and down to plot points Connect the 4 points with curve. Steps to write equation Find center Find radius Substitute into formula. Ex 3) Write the equation given the graph Ex 2) Graph (x-2)2 + (y+3)2 = 16 Center: (2, -3) Radius: Center: (-1, 1) Radius: 5 (x--1)2 + (y-1)2 = 52 (x+1)2 + (y-1)2 = 25 Circles

Cone cut by a plane at an angle through the sides Hyperbola Parabola Ellipse Cone cut by a plane at an angle through the sides Real World: Tunnels Cone cut by a plane perpendicular to the base Real World: tunnels Cone cut by a plane at an angle through the base and 1 side Real World: tunnels and overpasses