Circles
Zach Laughman, Jesse Nelson, Brandon Wright,
Samantha Huggins
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
Diameter
Start Angle
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
Standard Form
(X-h)^2 + (Y-k)^2 = r^2
(0,0)
(X-0)^2 + (Y-0)^2 = r^2
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
Rotated Form
When rotating a circle, the angle is the only part of the
circle that changes
90 degrees
Same circle, rotated angle
Circle Relationships
An angle outside of the circle can be used to help find
an angle within the circle
AxB = CxD
A(A+E) = C(C+F)
C
4(4+6) = 3(3+x)
Conic Form
The conic form of a circle is formed when you intersect
a double napped cone and a plane
Degenerate Case
The point as the radius approaches zero
Eccentricity
Says how round something is
The eccentricity of a circle is zero
Application
Science and Engineering
Radar systems, latitude/longitude, seismology (locating
where an earthquake started)