Circles Zach Laughman, Jesse Nelson, Brandon Wright, Samantha Huggins.

CirclesZach 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

Radius

Start Angle

Dia

mete

r

Cente

r

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

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)

A

B

C

D

46

10

3

E

F

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

X

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)