SWBAT: Write equations and graph circles in the coordinate ......SWBAT: Write equations and graph...

SWBAT: Write equations and graph circles in the coordinate plane.


x2 - 6x+ y2 – 2y = -4

(x2 - 6x ) + (y2 – 2y )= -4

+9 +1 +9 +1

(x2 -6x + 9) + (y2 – 2y + 1)= 6

(x-3)2 + (y-1)2 = 6

HINT: Make two perfect square trinomials, one with x and one with y.


Equation of a Circle(page 24)


Example 1: Writing the Equation of a Circle(page 24)

Model Problem:J with center J (2, 2) and radius 4

Center (h,k)

Center (2,2)

(x-h)2+(y-k)2=r2

(x-2)2+(y-2)2=42

(x-2)2+(y-2)2=16


Practice 1: Writing the Equation of a Circle(page 24)

L with center L (–5, –6) and radius 9

Center (h,k)

Center (-5,-6)

(x-h)2+(y-k)2=r2

(x-(-5))2+(y-(-6))2=92

(x+5)2+(y+6)2=81


Example 2: Identifying the Center/Radius from an Equation of a Circle(page 25)

Model Problem:

Center (h,k)

(x-h)2+(y-k)2=r2

(x-3)2+(y+5)2=9

(x-h)2+(y-k)2=r2

Think Opposite h=3 k=-5 r2=9 r=3

Center (3,-5)


Example 3: Identifying the center and radius from the graph of a circle. (Page 17)

Model Problem: Find the center and radius of the circle, and then write its equation. Center (h,k)

Center (-2,4)

RADIUS = 4

(x-h)2+(y-k)2=r2

(x-(-2))2+(y-4)2=42

(x+2)2+(y-4)2=16


Example 4: Writing the Equation of a Circle Given center and point (Page 25)

P with center P (0,-3) and passes through point (6,5).

h = 0 k = -3

Calculate the radius of the circle.

ΔX ΔY r2=a2+b2

0-6

-6

-3-5

-8

r2=(-6)2+(-8)2

r2=36+64

r2=100

r=10

x2+(y+3)2=100


Example 5: Writing the Equation of a Circle (Page 26)

Model Problem: Writing the equation of K that passes through endpoints A(5, 4) and B(1, –8).

Step 1: Calculate the Midpoint.

Step 2: Calculate the radius of the circle.

𝒎𝒊𝒅 = (𝟓+𝟏

𝟐,𝟒+−𝟖

𝟐)

𝒎𝒊𝒅 = (𝟔

𝟐,−𝟒

𝟐)

𝒎𝒊𝒅 = (𝟑,−𝟐)

ΔX ΔY c2=a2+b2

5-3

2

4-(-2)

6

c2=22+62

c2=4+36

c2=40

c=𝟐 𝟏𝟎


Example 4: Writing the Equation of a Circle (Page 26)

Model Problem: Writing the equation of K that passes through endpoints A(5, 4) and B(1, –8).

𝑪𝒆𝒏𝒕𝒆𝒓 = (𝟑,−𝟐)

r2=40

r=𝟐 𝟏𝟎

𝑪𝒆𝒏𝒕𝒆𝒓 = (𝒉, 𝒌)

(x-h)2+(y-k)2=r2

(x-3)2+(y-(-2))2=40

(x-3)2+(y+2)2=40


Practice #2: Writing the Equation of a Circle (Page 18)

Write the equation of circle Q that passes through (2, 3) and (2, –1)

Step 1: Calculate the Midpoint. Step 2: Calculate the radius of the circle.

(x-h)2+(y-k)2=r2

𝒎𝒊𝒅 = (𝟐, 𝟏)

ΔX ΔY 2-2

0

1-3

-2

r2=a2+b2

r2=(0)2+(-2)2

r2=4

r=2

(x-2)2+(y-1)2=4


x2 + y2 + 4x – 6y + 12 = 0

x2 + 4x+ y2 – 6y = -12

(x2 + 4x ) + (y2 – 6y )= -12

+4 +9 +9 +4

(x2 + 4x + 4) + (y2 – 6y + 9)= 1

(x+2)2 + (y-3)2 = 1


(x2 + 6x ) + (y2 – 8y )= -24

+9 +16

(x2 + 4x + 9) + (y2 – 6y + 16)= 1

(x+3)2 + (y-4)2 = 1


Practice #7: Graphing Circles (Page 28)

Graph x2 + y2 = 16.

(x-h)2+(y-k)2=r2

. .

. . . Center (0,0)

Radius = 4


Practice #6: Graphing Circles (Page 19)

(x-h)2+(y-k)2=r2

Center (-5,2) Radius = 2

(x + 5)2 + (y - 2)2 = 4

SWBAT: Write equations and graph circles in the coordinate ......SWBAT: Write equations and graph...

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