Circle

Definition: Let C be a point (ordered pair) and R a distance (number).
A circle is all the points distance R from point C. The circle has radius R and center C.

The equation of a circle with radius=R and center point at C=(0,0) is: x^2+y^2=R^2 .

\color{green}{ x^2+y^2=4}

\color{blue}{ x^2+y^2=10}

\color{purple}{ x^2+y^2=14400}

Here R^2=4 .

So radius = R = \sqrt{4}=2 .

The green circle is all points

distance=2 from center (0,0).

Here R^2=10 .

So radius = R = \sqrt{10}\approx 3.16 .

The blue circle is all points

distance= \sqrt{10} from center (0,0).

Here R^2=14400 .

So radius = R = \sqrt{14400}= 120 .

The purple circle is all points

distance=120 from center (0,0).

Level 2: Circle with radius=R and Center C=(p,q) .

The equation of a circle with radius=R and center point at C=(p,q) is: (x-p)^2+(y-q)^2=R^2 .

\color{green}{ (x-2)^2+y^2=4}

\color{blue}{ (x+4)^2+(y-2)^2=10}

\color{purple}{ (x+50)^2+(y+50)^2=14400}

Center is C=(2,0) and R^2=4 .

So radius = R = \sqrt{4}=2 .

The green circle is all points

distance=2 from (2,0)

Center is C=(-4,2)and R^2=10 .

So radius = R = \sqrt{10}\approx 3.16 .

The blue circle is all points

distance= \sqrt{10} from (-4,2).

Center is C=(-50,-50) and R^2=14400 .

So radius = R = \sqrt{14400}= 120 .

The purple circle is all points

distance=120 from (-50,-50).