SWBAT: Write equations and graph circles in the coordinate plane.
from standard form.
SWBAT: Write equations and graph circles in the coordinate plane.
Warm - Up
SWBAT: Write equations and graph circles in the coordinate plane.
SWBAT: Write equations and graph circles in the coordinate plane.
(x – h)2 + (y – k)2 = r2
Center = (h, k)
Center = (-5, 1); radius = 3
SWBAT: Write equations and graph circles in the coordinate plane.
(x – h)2 + (y – k)2 = r2
(x – 7)2 + (y – -3)2 = 42
SWBAT: write the equation of a circle from standard form to centerradius form.
SWBAT: write the equation of a circle from standard form to center-radius form.
Teacher Modeled
x2 + 8x + y2 – 2y = 64
x2 + 8x + 16 + y2 – 2y + 1 = 64 + 16 + 1
(x + 4)2 + (y - 1)2 = 81
𝒃
𝟐
𝟐
𝒃
𝟐
𝟐
→
→
𝟖
𝟐
−𝟐
𝟐
𝟐
= 𝟏𝟔
𝟐
=𝟏
Center = (-4, 1)
r = 𝟖𝟏 = 𝟗
SWBAT: write the equation of a circle from standard form to centerradius form.
.
Graph (x + 4)2 + (y - 1)2 = 81
(x-h)2+(y-k)2=r2
Center (-4,1)
Radius = 9
.
.
.
SWBAT: write the equation of a circle from standard form to centerradius form.
Student Try It
x2 + 24x + y2 + 6y = -137
x2 + 24x + 144 + y2 + 6y + 9 = -137 + 144 + 9
(x + 12)2 + (y + 3)2 = 16
𝒃
𝟐
𝟐
𝒃
𝟐
𝟐
→
→
𝟐𝟒
𝟐
𝟔
𝟐
𝟐
= 𝟏𝟒𝟒
𝟐
=𝟗
Center = (-12, -3)
r = 𝟏𝟔 = 𝟒
SWBAT: write the equation of a circle from standard form to centerradius form.
Graph (x + 12)2 + (y + 3)2 = 16
(x-h)2+(y-k)2=r2
Center (-12,-3)
Radius = 4
SWBAT: write the equation of a circle from standard form to centerradius form.
x2 - 2x + y2 + 4y = 4
x2 - 2x + 1 + y2 + 4y + 4 = 4 + 1 + 4
(x - 1)2 + (y + 2)2 = 9
𝒃
𝟐
𝟐
𝒃
𝟐
𝟐
→
−𝟐
𝟐
𝟒
→
𝟐
𝟐
=𝟏
𝟐
=𝟒
Center = (1, -2)
r= 𝟗=𝟑
SWBAT: write the equation of a circle from standard form to centerradius form.
Graph (x - 1)2 + (y + 2)2 = 9
(x-h)2+(y-k)2=r2
Center (1,-2)
Radius = 3
SWBAT: write the equation of a circle from standard form to centerradius form.
x2 + 6x + y2 - 2y = -1
x2 + 6x + 9 + y2 - 2y + 1 = -1 + 9 + 1
(x + 3)2 + (y - 1)2 = 9
𝒃
𝟐
𝟐
𝒃
𝟐
𝟐
→
𝟔
𝟐
→
−𝟐
𝟐
𝟐
=𝟗
𝟐
=𝟏
Center = (-3, 1)
r= 𝟗=𝟑
SWBAT: write the equation of a circle from standard form to centerradius form.
Graph (x + 3)2 + (y - 1)2 = 9
(x-h)2+(y-k)2=r2
Center (-3,1)
Radius = 3
SWBAT: write the equation of a circle from standard form to centerradius form.
x2
x2
+ x +
𝟏
𝟒
+x + +
(x +
𝒃
𝟐
𝟐
𝒃
𝟐
𝟐
→
𝟏
𝟐
→
−𝟏
𝟐
𝟐
𝟏
=
𝟒
𝟐
𝟏
=
𝟒
𝟏 2
)
𝟐
y2
y2
- y =
𝟏
𝟒
𝟏
𝟐
𝟏
𝟐
𝟏
𝟒
- y+ = + +
+ (y -
𝟏 2
)
𝟐
𝟏
𝟒
=1
Center = (r= 𝟏=𝟏
𝟏 𝟏
, )
𝟐 𝟐
SWBAT: write the equation of a circle from standard form to centerradius form.
Graph (x +
𝟏 2
)
𝟐
+ (y -
(x-h)2+(y-k)2=r2
Center (-½,½)
Radius = 1
𝟏 2
)
𝟐
= 1
SWBAT: write the equation of a circle from standard form to centerradius form.
a. Center = (2, 3); 𝒓 =
𝟐−𝟓
𝟐
+ 𝟑−𝟕
𝟐
=𝟓
(x - 2)2 + (y - 3)2 = 25
b. Center = (-1, -1); 𝒓 =
−𝟏 − 𝟓
𝟐
+ −𝟏 − 𝟕
𝟐
= 𝟏𝟎
(x + 1)2 + (y + 1)2 = 100
SWBAT: write the equation of a circle from standard form to center-radius form.
c. 𝒎𝒓𝒂𝒅𝒊𝒖𝒔 𝒐𝒇 𝒄𝒊𝒓𝒄𝒍𝒆𝒔 =
𝟒
𝟑
𝟑
𝒎⊥ = −
𝟒
Pt of tangency (5, 7)
y-y1=m(x-x1)
y =
3
7=− 5 +
4
15
7 = − +𝑏
4
43
=𝑏
4
3
43
− 𝒙+
4
4
𝑏
y–7=
y–7=
3
− (x
4
3
−
4
- 5)
(x - 5)
SWBAT: write the equation of a circle from standard form to centerradius form.
SWBAT: write the equation of a circle from standard form to centerradius form.
x2 - 2x + y2 + 6y = -3
𝒄𝒙 :
𝒄𝒚 :
−𝟐 𝟐
𝟐
𝟔 𝟐
𝟐
=𝟏
=𝟗
x2 - 2x + 1 + y2 + 6y + 9 = -3 + 1 + 9
(x - 1)2 + (y + 3)2 = 7