7.1: Equations of Circles

LT: How do we use completing the square to create Equations of Circles

SC: I will be able to Identify center and radius of a circle. Write an equation of a circle from a graph, and rewrite an equation in standard form.

Open Ended

Speak up/Speak out

Completing the square actually creates what important math formula

Circle

• A collection of all points (x, y) that are equidistant from a fixed point (h, k)

• Radius ( r ) - the distance between the center and all points (x, y) on the circle

• Center: (h, k)

Standard From of a Circle

Multiple Choice

What is the radius and center of

$$\left(x-9\right)^2+\left(y+3\right)^2=49$$  

• (9, -3); r = 7

• (9, 3); r = 7

• (9, -3); r = 49

• (-9, -3); r = 7

Multiple Choice

What is the center and radius of

$$\left(x+1\right)^2+\left(y+2\right)^2=10$$  

• (-1, -2); r = 10

• (-1, -2); r =  $$\sqrt{10}$$  

• (1, 2); r = 10

• (1, 2); r =  $$\sqrt{10}$$  

Multiple Choice

What is the center and radius of

$$x^2+y^2=9$$  ?

• (3, 3); r = 3

• (0, 0); r = 9

• (0, 3); r = 3

• (0, 0); r = 3

Completing the Square

To get a Circle Equation in Standard form to identify the center and radius, we use completing the square.

​The "shortcut"

Completing the Square with One Variable

Open Ended

Accountability:

If the "b" value is odd, should you make half of it a fraction or a decimal?

Why?

Multiple Choice

Complete the Square

$$x^2+6x+8=0$$  

• $$\left(x-3\right)^2=-8$$  

• $$\left(x+3\right)^2=17$$  

• $$\left(x+3\right)^2=1$$  

• $$\left(x-3\right)^2=8$$  

Multiple Choice

Complete the square

$$y^2-12y+9=0$$  

• $$\left(y+6\right)^2=9$$  

• $$\left(y+6\right)^2=27$$  

• $$\left(y-6\right)^2=45$$  

• $$\left(y-6\right)^2=27$$  

Completing the Square with two variables

​A step by step example of completing the square to make a circle. Below: this is called General Form.

​This above is the Standard Form.

Multiple Choice

What is the center of

$$x^2+y^2+6x-8y-11=0$$  

• (6, 0)

• (-3, 4)

• (4, -3)

• (3, 4)

Multiple Choice

What is the radius of

$$x^2+y^2-2x+6y-10=0$$  

• $$20$$  

• $$0$$  

• $$\sqrt{10}$$  

• $$\sqrt{20}$$  

Word Cloud

How many boxes do you need to have on the right side of the equation?

One or two or depends?

Multiple Choice

What is the center of the circle whose endpoints of the diameter are (-4, 1) and (4, 5)

• (0, 0)

• (0, 3)

• (3, 0)

• (4, 5)

Poll

Ownership:

My feelings after this lesson

• 1) It's really hard, I need more practice

• 2) I get it, but I'm making careless mistakes

• 3) This is right up my alley.