Writing and Graphing Equations of Circles

Graphing Circles: Standard and General Form

Standard Form

 $\left(x-h\right)^{2\ }+\left(y-k\right)^{2\ }=r^2$  

Center: (h, k)

Radius:  $\sqrt{r^2}=r$   

Example 1 Find the Center and Radius of the Circle

 $\left(x-4\right)^{2\ }+\left(y+2\right)^{2\ }=81$  

Center: (4, -2)    *note: change the signs from the equation*

Radius:  $\sqrt{81}=9$  

Multiple Choice

What is the center and radius of the circle?

$$\left(x+5\right)^2+\ \left(y+1\right)^{2\ }=4$$  

• Center: (5, 1) 
  
  Radius: 4

• Center (5, 1)
  
  Radius: 2

• Center (-5, -1) 
  
  Radius: 4

• Center (-5, -1) 
  
  Radius: 2

Multiple Choice

What is the center and radius of the circle?

$$\left(x-3\right)^2+\ \left(y+9\right)^{2\ }=16$$  

• Center: (3, -9) 
  
  Radius: 4

• Center (3, 9)
  
  Radius: 4

• Center (-3, 9) 
  
  Radius: 4

• Center (3, -9) 
  
  Radius: 16

General Form

 $ax^2+by^2+cx+dy+e=f$  

How to change general form into standard form:
Step 1: Move "e" to the right side of the equal sign
Step 2: Group x's together. Group y's together.
Step 3: Divide "c" and "d" by 2 and square it.
Step 4: Add the "squared" number to both sides of the equal sign.
Step 5: Factor and solve.

General Form to Standard Form

Step 1: Move "e" to the right side of the equal sign

Step 2: Group x's together. Group y's together.

Step 3: Divide "c" and "d" by 2 and square it.

Step 4: Add the "squared" number to both sides of the equal sign.

Step 5: Factor and solve.

Multiple Choice

What is the center of the circle?

$$x^2+y^2-4x+22y+116=0$$  

• $$\left(-4,\ 22\right)$$  

• $$\left(2,\ -11\right)$$  

• $$\left(-2,\ 11\right)$$  

• $$\left(4,\ -22\right)$$  

Multiple Choice

What is the equation of the circle written in standard form?

$$x^2+y^2+14x+18y+114=0$$  

• $$\left(x-7\right)^2+\left(y+9\right)^2=16$$  

• $$\left(x+7\right)^2+\left(y+9\right)^2=16$$  

• $$\left(x+7\right)^2+\left(y+9\right)^2=244$$  

• $$\left(x-7\right)^2+\left(y+9\right)^2=244$$  

Poll

How do you feel after seeing this lesson?

• Confident

• I need more practice

• I need help!