Topic: Section:
9 2
Equations of Circles .
Questions/Main
Examples & Notes
Ideas
Equation of a Standard Form
Circle
Center: _______
(𝒙 − 𝒉)𝟐 + (𝒚 − 𝒌)𝟐 = 𝒓𝟐
(n1 -- Radius: _____
Writing Fill in the missing information from the table.
Equations of Center Radius Equation
Circles 1)2 +
(1,5) 4 (X (y 5) 1
-
=
-
(2,9) 2 (x 2)2 + (y 9) 4
- -
=
(-4, 7) 9 (X + 4) +
(y 7)2
-
= 8)
(-8, -3) 12 (x + z)2 +
(y 3)2 144
+ =
(4 -3),
25 = 5 (𝒙 − 𝟒)𝟐 + (𝒚 + 𝟑)𝟐 = 𝟐𝟓
(0 14) ,
T9 (𝒙 + 𝟏)𝟐 + (𝒚 − 𝟏𝟒)𝟐 = 𝟏𝟗
(9 , 11) (𝒙 + 𝟗)𝟐 + (𝒚 + 𝟏𝟏)𝟐 = 𝟑𝟏
10 ,
0) =
7 (X -
0)2 𝒙𝟐 + 𝒚𝟐 = 𝟒𝟗
Given the Center Write the equation of a circle with the following characteristics.
X, Y X2 Yz
and a Point 1. Center at (9, 10) and passing through (7, 4)
To write equation : r =
(1 9) (4 10)2 -
+ -
Equation
① NeedCenter - 2
( 6) (x 9) (y 10) (o)and
+ -
-
=
-
+
of radius
②Length r=
30
+
taly-1040 (i)
= xx) + (yz y ) v
- no,
=
2. Center at (1, -5) and passing through (-7, -13)
=
+ ( 3 5)
/
r +
+
F 8
r ( 8)
= + (y 5) + + = 128
= 64
=
9 2
Equations of Circles .
Questions/Main
Examples & Notes
Ideas
Equation of a Standard Form
Circle
Center: _______
(𝒙 − 𝒉)𝟐 + (𝒚 − 𝒌)𝟐 = 𝒓𝟐
(n1 -- Radius: _____
Writing Fill in the missing information from the table.
Equations of Center Radius Equation
Circles 1)2 +
(1,5) 4 (X (y 5) 1
-
=
-
(2,9) 2 (x 2)2 + (y 9) 4
- -
=
(-4, 7) 9 (X + 4) +
(y 7)2
-
= 8)
(-8, -3) 12 (x + z)2 +
(y 3)2 144
+ =
(4 -3),
25 = 5 (𝒙 − 𝟒)𝟐 + (𝒚 + 𝟑)𝟐 = 𝟐𝟓
(0 14) ,
T9 (𝒙 + 𝟏)𝟐 + (𝒚 − 𝟏𝟒)𝟐 = 𝟏𝟗
(9 , 11) (𝒙 + 𝟗)𝟐 + (𝒚 + 𝟏𝟏)𝟐 = 𝟑𝟏
10 ,
0) =
7 (X -
0)2 𝒙𝟐 + 𝒚𝟐 = 𝟒𝟗
Given the Center Write the equation of a circle with the following characteristics.
X, Y X2 Yz
and a Point 1. Center at (9, 10) and passing through (7, 4)
To write equation : r =
(1 9) (4 10)2 -
+ -
Equation
① NeedCenter - 2
( 6) (x 9) (y 10) (o)and
+ -
-
=
-
+
of radius
②Length r=
30
+
taly-1040 (i)
= xx) + (yz y ) v
- no,
=
2. Center at (1, -5) and passing through (-7, -13)
=
+ ( 3 5)
/
r +
+
F 8
r ( 8)
= + (y 5) + + = 128
= 64
=
