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

## Presentation on theme: "Circles Zach Laughman, Jesse Nelson, Brandon Wright, Samantha Huggins."— Presentation transcript:

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: 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 = CxD A(A+E) = C(C+F) A B C D 4 6 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)

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