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## PowerPoint Slideshow about ' Circles' - sancha

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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
- 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

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:

- 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

- 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

- 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

- 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)

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