Alg2Hon 10­1 and 10­3 Notes and answers.notebook

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April 29, 2013

Apr 28­3:36 PM

10­1 Exploring Conic SectionsConic sections are used to describe all the possible ways a plane and a double right cone can intersect.

First studied in ancient Greece from 600­300 BC

To get a circle, ellipse, parabola or hyperbola, the plane does NOT pass through the vertex of the double­right cone.

http://www.shodor.org/interactivate/activities/CrossSectionFlyer/

Apr 28­3:46 PM

degenerate conics: the plane DOES pass through the vertex making a point, line, or intersecting lines

Alg2Hon 10­1 and 10­3 Notes and answers.notebook

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April 29, 2013

Apr 28­3:52 PM

Example 1: x2 + y2 = 16

conic section:

center: radius:

line(s) of symmetry:

domain:

range:

x­intercept(s):

y­intercept(s):

Apr 28­3:56 PM

Example 2: 27x2 + 3y2 = 27

conic section:

center:

line(s) of symmetry:

domain:

range:

x­intercept(s):

y­intercept(s):

Alg2Hon 10­1 and 10­3 Notes and answers.notebook

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April 29, 2013

Apr 28­3:57 PM

Example 3: x2 ­ y2 = 16

conic section:

center:

line(s) of symmetry:

domain:

range:

x­intercept(s):

y­intercept(s):

Apr 28­4:06 PM

(x,y)

(h,k)Standard form of an equation of a circle with center (h,k) and radius r:

The length of the radius equals the distance between the center (h,k) and the point (x,y).

circle: the set of all points in a plane that are equidistant from a given point called the center

radius: a segment whose endpoints are the center of the circle and

any point on the circle.

10­3 Circles

When the center of the circle is (0, 0), you get x2 + y2 = r2

concentric circles ­ have the same center but not necessarily the same radius

Alg2Hon 10­1 and 10­3 Notes and answers.notebook

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April 29, 2013

Apr 28­4:16 PM

Example 1: (p. 631) Got It? 1 What is an equation of the circle with center (5, ­2) and radius 8?

Apr 28­4:17 PM

Example 2: (p. 631) Got It? 2What is an equation for each translation? Graph the given equation and the translation.a. x2 + y2 = 1; left 5 units and down 3 units

b. x2 + y2 = 9; right 2 units and up 3 units

Alg2Hon 10­1 and 10­3 Notes and answers.notebook

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April 29, 2013

Apr 28­4:22 PM

Example 3: (p. 632) Got It? 3aWhat is an equation of the circle for a circular irrigation field that has radius 12 and center (7, ­10)?

Apr 28­4:24 PM

Example 4 (p. 633) Got It? 4What are the center and radius of the circle with the given equation?a. (x + 8)2 + (y + 3)2 = 121

b. x2 + y2 ­ 6x + 14y = 8

c. (Additional example) x2 + y2 + 2x ­ 6y = 6

Alg2Hon 10­1 and 10­3 Notes and answers.notebook

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April 29, 2013

Apr 28­4:29 PM

Example 5 (p. 633) Got It? 5What is the graph of (x ­ 4)2 + (y+2)2 = 49?

Apr 28­4:44 PM

Example 6Use the given information to write an equation of a circle.

(­5, 2) and (3,6) are endpoints of a diameter

Alg2Hon 10­1 and 10­3 Notes and answers.notebook

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April 29, 2013

Apr 28­4:00 PM

Practice(p. 618) 22, 25 and same directions for

(p. 634) 10, 15, 16, 20, 28, 30, 38, 46, 50, 54­62 even