10.1,2,3 1

Sections 10.1-10.3 Conic Sections

Circles Parabolas Ellipses Hyperbolas

10.1,2,3 2

Introduction to Conic Sections Parabola Circle Ellipse Hyperbola

10.1,2,3 3

Ax2 + By2 + Cxy + Dx +Ey + F = 0 The constants A, B, C, D, E and F determine

the nature of the graphs formed For conic sections, A and B cannot both be 0

10.1,2,3 4

Remember Parabolas? Two styles: Functions & Relations

Find the Vertex:x = -b/(2a),

(or y = -b/(2a))solve for y or x

10.1,2,3 5

A Circle has a Center and a Radius

Find the center & radius

10.1,2,3 6

Sketch a circle: (double “complete the square”)

Find the Center and Radius

4.12)1,4(

2)1()4(

116151248

??15?2?8

01528

22

2222

2122

12

22

radiuscenter

yx

yyxx

yyxx

yxyx

10.1,2,3 7

An Ellipse also has a Center and Foci

10.1,2,3 8

Graphing an Origin-Centered Ellipse

10.1,2,3 9

An Ellipse Centered at (h,k)

10.1,2,3 10

Hyperbolas have Two Branches

10.1,2,3 11

A Hyperbola Centered at the Origin

10.1,2,3 12

Non-Standard Hyperbola

10.1,2,3 13

What Next? The Final Exam