CIRCLES IN THE COORDINATE PLANE

Circle in the Coordinate Plane

Circle with Center (0,0) and radius (r)

• Standard Form

   $x^2\ +\ y^2\ =\ r^2$ 

• Ex: $center\ \left(0,0\right)\ and\ radius\ =\ 5\ units$  

• Standard form:  $x^2+y^2=\ 5^2\ \ or\ x^2+y^2=25$  

•  $General\ Form:\ x^2+y^2-25=0$  

What is the center?

What is the radius?

• C (0,0)

• r= 3

• Standard Form:

   $x^2+y^2=9$  
  

• General Form:  $x^2+y^2-9=0$  

What is the center?

What is the radius?

• C( 0,0)

• r=5

• Standard Form:

   $x^2+y^2=25$  
  

• General Form:  $x^2-y^2-25=0$  

Multiple Choice

Find the standard form of a circle if the center is at ( 0,0) and radius of 12 units.

•  $x^2+y^2=\ 12$  

•  $x^2+y^2=144$  

•  $x^2-y^2=\ 144$  

Multiple Choice

What is the general form of a circle whose center is at (0,0) and radius of 3 units

• $x^2+y^2=9$

• $x^2+y^2=3$

• $x^2+y^2-9=0$

Multiple Choice

What is the radius of the circle whose standard form is

 $x^2+y^2=\ 36$  

• 6

•  $\sqrt{6}$  

• 36

Multiple Choice

What is the radius of the circle if the standard form is 

 $x^2+y^2=\ 2$  

•  $\sqrt{2}$  

• 2

•  $4$  

Circle with center at (h,k) and radius (r)

Standard form:

 $\left(x\ -\ h\right)\ ^2\ +\ \left(y-k\right)^2=\ r^2$  
General form:
 $Ax^2+By^2+Cx\ +Dy\ +\ E=\ 0$  

What is the center? What is the radius?

• C( 1, -2)

• r= 2 units

• Standard Form: 

   $\left(x-1\right)^2+\ \left(y+2\right)^2=\ 4$  

Ex: Center (1,-2) radius= 2

 units

• Standard Form:

   $\left(x\ -1\right)^2\ +\ \left(y+2\right)^2=\ 4$  

• General form:  $\left(\ x^2\ -2x\ +\ 1\right)\ +\ \left(\ y^2\ +\ 4y+\ 4\right)=\ 4$  Combining and Arranging the terms:

•  $x^2\ +\ y^2\ -\ 2x\ +\ 4y\ +1\ =\ 0$