Graphs and Equations of Circles

Book: Math 3

(Green Book)

Section: 5.2

Standard Equation of a Circle

What do you think we need to write an equation of a circle? Radius Center Point on a Circle

Let’s See What We Know

The point (6, 2) lies on a circle whose center is at the origin. Find the radius. What formula do we

need to use in order to find the radius?

DISTANCE FORMULA!!!!!!!

2 2

2 1 2 1d x x y y

2 26 0 2 0r

2 26 2

36 4

40

r

r

r

Let’s See What We Know

The point (-2, -2) lies on a circle whose center is at (4, -5). Find the radius.

2 2

2 2

2 4 2 ( 5)

6 3

36 9

45

r

r

r

r

Let’s Make Some Observations

2 2 25x y

What’s the Radius?

Where is the center?

Here is the equation, how is it related to the circle?

Let’s Make Some Observations

What’s the Radius?

Where is the center?

Here is the equation, how is it related to the circle?

2 24 5 16x y

So we have determined…

Let the center of a circle be the point (h,k) and the radius be r

From our observations we have determined that the standard equation of a circle is:

2 2 2x h y k r

Write the Equation of the Circle

2 2 9x y

Write the Equation of the Circle

2 22 4 36x y

Graph the Circle

2 2 144x y

Graph the Circle

2 23 3 150x y

Graph the Circle

2 23 2 81x y

Write the Equation of the Circle

Center: origin Radius: 5

Center: (4, -2) Radius: 7

Homework

GREEN BOOK

Pg. 182 #1 – 22 WS

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From the worksheet