SWBAT: Write equations and graph circles in the coordinate plane.
SWBAT: Write equations and graph circles in the coordinate plane.
HINT:
Make two perfect
square trinomials, one
with x and one with y.
x2 - 6x+ y2 – 2y = -4
(x2 - 6x
) + (y2 – 2y
)= -4
+9
+9
+1
(x2 -6x + 9) + (y2
+1
– 2y + 1)= 6
(x-3)2 + (y-1)2 = 6
SWBAT: Write equations and graph circles in the coordinate plane.
SWBAT: Write equations and graph circles in the coordinate plane.
Equation of a Circle(page 24)
SWBAT: Write equations and graph circles in the coordinate plane.
Example 1: Writing the Equation of a Circle(page 24)
Model Problem:J with center
Center (h,k)
Center (2,2)
J (2, 2) and radius 4
(x-h)2+(y-k)2=r2
(x-2)2+(y-2)2=42
(x-2)2+(y-2)2=16
SWBAT: Write equations and graph circles in the coordinate plane.
Practice 1: Writing the Equation of a Circle(page 24)
L with center L (–5, –6) and radius 9
(x-h)2+(y-k)2=r2
Center (-5,-6) (x-(-5))2+(y-(-6))2=92
(x+5)2+(y+6)2=81
Center (h,k)
SWBAT: Write equations and graph circles in the coordinate plane.
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-h)2+(y-k)2=r2
(x-3)2+(y+5)2=9
Think Opposite
h=3
k=-5
Center (3,-5)
r2=9
r=3
SWBAT: Write equations and graph circles in the coordinate plane.
Example 3: Identifying the center and radius from the graph of a circle. (Page 17)
Find the center and radius of the circle,
and then write its equation.
Center (h,k)
Center (-2,4)
Model Problem:
RADIUS = 4
(x-h)2+(y-k)2=r2
(x-(-2))2+(y-4)2=42
(x+2)2+(y-4)2=16
SWBAT: Write equations and graph circles in the coordinate plane.
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
0-6
-3-5
-6
-8
x2+(y+3)2=100
r2=a2+b2
r2=(-6)2+(-8)2
r2=36+64
r2=100
r=10
SWBAT: Write equations and graph circles in the coordinate plane.
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.
𝟓+𝟏 𝟒+−𝟖
𝒎𝒊𝒅 = (
,
)
𝟐
𝟐
𝟔 −𝟒
𝒎𝒊𝒅 = ( , )
𝟐 𝟐
𝒎𝒊𝒅 = (𝟑, −𝟐)
Step 2: Calculate the radius of the circle.
ΔX
ΔY
5-3
4-(-2)
2
6
c2=a2+b2
c2=22+62
c2=4+36
c2=40
c=𝟐 𝟏𝟎
SWBAT: Write equations and graph circles in the coordinate plane.
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)
𝑪𝒆𝒏𝒕𝒆𝒓 = (𝒉, 𝒌)
r2=40
r=𝟐 𝟏𝟎
(x-h)2+(y-k)2=r2
(x-3)2+(y-(-2))2=40
(x-3)2+(y+2)2=40
SWBAT: Write equations and graph circles in the coordinate plane.
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.
𝒎𝒊𝒅 = (𝟐, 𝟏)
Step 2: Calculate the radius of the circle.
ΔX
ΔY
r2=a2+b2
2-2
1-3
r2=(0)2+(-2)2
0
-2
r2=4
r=2
(x-h)2+(y-k)2=r2
(x-2)2+(y-1)2=4
SWBAT: Write equations and graph circles in the coordinate plane.
x2 + y2 + 4x – 6y + 12 = 0
x2 + 4x+ y2 – 6y = -12
(x2 + 4x
) + (y2 – 6y
)= -12
+9
+4
+9
(x2 + 4x + 4) + (y2
+4
– 6y + 9)= 1
(x+2)2 + (y-3)2 = 1
SWBAT: Write equations and graph circles in the coordinate plane.
(x2 + 6x
) + (y2 – 8y
(x2 + 4x + 9) + (y2
)= -24
+9
+16
– 6y + 16)= 1
(x+3)2 + (y-4)2 = 1
SWBAT: Write equations and graph circles in the coordinate plane.
Practice #7: Graphing Circles (Page 28)
Graph x2 + y2 = 16.
(x-h)2+(y-k)2=r2
Center (0,0)
Radius = 4
.
.. .
.
SWBAT: Write equations and graph circles in the coordinate plane.
Practice #6: Graphing Circles (Page 19)
(x + 5)2 + (y - 2)2 = 4
(x-h)2+(y-k)2=r2
Center (-5,2)
Radius = 2
SWBAT: Write equations and graph circles in the coordinate plane.
SWBAT: Write equations and graph circles in the coordinate plane.
SWBAT: Write equations and graph circles in the coordinate plane.