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