Circle Investigation

In class we came up with a definition for any circle and a standard form for the equation of a circle.

We defined a circle as the set of all points (x,y) in a plane that are equidistant from a fixed point, called the center of the circle. The distance between the center and any point (x.y) on the circle is the radius, r.

Using the distance formula, the distance between the center, we defined as the point with coordinates (h,k) and any point (x,y) on the circle is

Part One: Transformations

Video One

Video Two

Video Three

In each of these video investigations, describe your observations of what happens to the circle as n increases, decreases, and what n correlates to in the equation.

Part Two:

For each of these circles, find the center and radius. Then come up with an equation for each of the circles. (Number One and Two)

Number One:

Number Two:

Number Three:

A.) Find the Centers and radii on circles A, B, C, F, G to come up with its corresponding standard equation form.

B.) Discuss observations you see with these particular circles.

C.) Think about what would happen if we made a polygon by connecting ABFEDC:

D.) What type of polygon would it be and what is special about it?

Homework Challenge: Using a common household object, trace it anywhere on a defined coordinate plane. See if you can then come up with its circle equation.