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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

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Presentation Transcript
circles

Circles

Zach Laughman, Jesse Nelson, Brandon Wright, Samantha Huggins

key words
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
slide3

Diameter

Radius

Start Angle

Center

origin and construction
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
Standard Form
  • (X-h)^2 + (Y-k)^2 = r^2

(0,0)

  • (X-0)^2 + (Y-0)^2 = r^2
geometric algebraic form
Geometric/Algebraic Form
  • X^2 + Y^2 + aX + bY + c = 0
  • Get this form into Standard Form by completing the square

Complete the Square:

  • Get all X’s and Y’s on the left side
  • Get all constants on the right side
  • Take half of the middle number, square it, and add it to both sides (for X and Y)
  • Simplify
rotated form
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

circle relationships
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)

4(4+6) = 3(3+x)

B

10

6

E

A

4

C

3

F

X

D

13.333

conic form
Conic Form
  • The conic form of a circle is formed when you intersect a double napped cone and a plane
degenerate case
Degenerate Case
  • The point as the radius approaches zero
eccentricity
Eccentricity
  • Says how round something is
  • The eccentricity of a circle is zero
application
Application
  • Science and Engineering
  • Radar systems, latitude/longitude, seismology (locating where an earthquake started)
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