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CirclesZach Laughman, Jesse Nelson, Brandon Wright, Samantha Huggins
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Key Words
Radius- a straight line from the center to the circumference of a circle of sphere
Diameter- the distance from one end of circle to another
Circumference- the enclosing boundary of a circle
-the distance around a circle
Start Angle- The angle in a circle at which you start to determine the degree of another angle
Center- the middle point of the circle
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Radius
Start Angle
Dia
mete
r
Cente
r
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Origin and Construction
Origin: a slice parallel to the base of a cone (see figure)
Construction: a circle is made up of points that are equidistance from the origin
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Standard Form
(X-h)^2 + (Y-k)^2 = r^2
(0,0)
(X-0)^2 + (Y-0)^2 = r^2
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Geometric/Algebraic Form
X^2 + Y^2 + aX + bY + c = 0
Get this form into Standard Form by completing the square
Complete the Square:
1) Get all X’s and Y’s on the left side
2) Get all constants on the right side
3) Take half of the middle number, square it, and add it to both sides (for X and Y)
4) Simplify
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Rotated Form
When rotating a circle, the angle is the only part of the circle that changes
Same circle, rotated angle
90 degrees
135 degrees
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Circle Relationships
An angle outside of the circle can be used to help find an angle within the circle
AxB = CxDA(A+E) = C(C+F)
A
B
C
D
46
10
3
E
F
4(4+6) = 3(3+x)
X
13.333
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Conic Form
The conic form of a circle is formed when you intersect a double napped cone and a plane
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Degenerate Case
The point as the radius approaches zero
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Eccentricity
Says how round something is
The eccentricity of a circle is zero
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Application
Science and Engineering
Radar systems, latitude/longitude, seismology (locating where an earthquake started)