CCGPS GEOMETRY

UNIT QUESTION: How are the equations of circles and parabolas derived?Standard: MCC9-12..A.REI.7, G.GPE.1,2 and 4

Today’s Question:How is the equation of a circle derived?Standard: MCC9-12..G.GPE.1

EOCT PRACTICE QUESTION

Use the Quadratic formula to find the solutions to the following quadratic equation:

a.) c.)

b.) d.)

CIRCLE:

What are the coordinates of this circle’s center?

What is its radius?

EQUATIONS OF CIRCLES

Standard Form of a CircleCircle with center at the origin (0,0)

Standard form of a circle that is translated

**Center: (h, k) Radius: r **

2 2 2x y r

2 2 2( )x h y k r

FINDING THE EQUATION OF A CIRCLE

Write the standard form of the equation for the circle that has a center at the origin and has the given radius. 1. r = 9 2. r = 14 3. 31

WRITING EQUATIONS OF CIRCLES

Write the standard equation of the circle:

Center (4, 7) Radius of 5

(x – 4)2 + (y – 7)2 = 25

Write the standard equation of the circle:

Center (-3, 8) Radius of 6.2

(x + 3)2 + (y – 8)2 = 38.44

Writing Equations of Circles

WRITING EQUATIONS OF CIRCLES

Write the standard equation of the circle:

Center (2, -9) Radius of

(x – 2)2 + (y + 9)2 = 11

11

EQUATION OF A CIRCLE

The center of a circle is given by (h, k).The radius of a circle is given by r.The equation of a circle in standard form is (x – h)2 + (y – k)2 = r2

GRAPHING CIRCLES

(x – 3)2 + (y – 2)2 = 9

Center (3, 2)

Radius of 3

GRAPHING CIRCLES

(x + 4)2 + (y – 1)2 = 25

Center (-4, 1)

Radius of 5

GRAPHING CIRCLES

(x – 5)2 + y2 = 36

Center (5, 0)

Radius of 6

2 2

2 2

( 8 ) 7

( 8 6) 171 6

x x y

x x y

Graphing a circle in Standard Form!!

Example:

2 2 8 7 0x y x

Center: (4, 0) r: 3

To write the standard equation of a translated circle, you may need to

complete the square.

Standard Form!! 2 2( 4) 9x y

WRITE THE STANDARD EQUATION FOR THE CIRCLE. STATE THE CENTER AND RADIUS.

2 2 4 6 3 0x y x y

Write the standard equation for the circle. State the center and radius.

2 22 2 16 4 20 0x y x y

: (4, 1)

: 7

Center

Radius