DIVISION OF RIZAL
Center- Radius of the Circle
WEEK 4 LESSON 1
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
Objectives:
You are expected to
1.Illustrates center-radius form of the equation of
the circle ;
2.Determines the center-radius form of the
equation of a circle given its equation and vice
versa and;
3.Graphs a circle and other geometric figures on
the coordinate plane.
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
Standard equation of the circle
If the circle is at the origin
x2+y2=r2
If the circle is not at the origin
 x  h
2
 y  k  r 2
2
The center is at (h, k)
where r is the length of the radius
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
5
5
5
5
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
Find the center, radius, & equation of the circle.
The center is (0, 0)
The radius is 12
The equation is
x2 + y2 = 144
CASIMIRO A. YNARES SR. MNHS
Find the center,
and radius if the
equation is given
DIVISION OF RIZAL
C (0,0) r = 5
1)
2
x
+
2
y
= 25
25 = 5
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
C (0,0) r = 1
2)
2
x
+
2
y
=1
1=1
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
C (0,0) r = 11
3)
2
x
+
2
y
= 121
121 = 11
CASIMIRO A. YNARES SR. MNHS
Find the equation
if the center &
radius is given
DIVISION OF RIZAL
C (0,0) r = 9
4.)
2
x
+
2
y
= 81
81 = 9
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
 x  h
2
 y  k  r
2
CASIMIRO A. YNARES SR. MNHS
2
DIVISION OF RIZAL
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
Write the standard form for the equation of a
circle with center (3, -2) and a radius of 4.
 x  h +  y  k 
2
2
 x  3  +  y   2  
2
 x  3
2
r
2
2
4
2
+  y  2   16
CASIMIRO A. YNARES SR. MNHS
2
DIVISION OF RIZAL
Write an equation of a circle with center
(-4, 0) and a diameter of 10.
 x  h +  y  k 
2
2
 x   4  +  y  0
2
x
 4
2
+y
2
r
2
2
2
5
 25
CASIMIRO A. YNARES SR. MNHS
Find the center,
and radius if the
equation is given
DIVISION OF RIZAL
C (9,0) r = 10
(x–9
2
)
+
2
y
CASIMIRO A. YNARES SR. MNHS
= 100
DIVISION OF RIZAL
C (-5,0) r = 12
( x+
2
5)
+
2
y
= 144
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
C (0,3) r = 11
2
x
+(y–3
2
)
= 121
CASIMIRO A. YNARES SR. MNHS
Find the equation
if the center &
radius is given
DIVISION OF RIZAL
C (0,-1) r = 5
2
x
+ ( y +1
2
)
= 25
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
C (9,4) r = 1
(x–9
2
)
+ (y–4
2
)
CASIMIRO A. YNARES SR. MNHS
=1
DIVISION OF RIZAL
C (0,-2) r = 13
2
x
+( y+2
2
)
= 169
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
C (-7,6) r = 5
(x+7
2
)
+(y–6
2
)
CASIMIRO A. YNARES SR. MNHS
= 25
DIVISION OF RIZAL
DIVISION OF RIZAL
graph
The center is
(1, -3)
The radius is
7
The equation is
(x – 1)2 + (y + 3)2 = 49
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
Graph the circle, identify the center & radius.
(x – 3)2 + (y – 2)2 = 9
Center (3, 2)
Radius of 3
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
Converting from General Form to Standard
1. Move the x terms together and the y
terms together.
2. Move C to the other side.
3. Complete the square (as needed) for x.
4. Complete the square(as needed) for y.
5. Factor the left & simplify the right.
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
2. Write the standard equation of the circle. State the
center & radius.
8/2 = 4
2
4 = 16
x  y  8x  7  0
2
2
( x  8x
)  y  7
2
2
( x  8 x  16)  y  7  16
2
2
( x  4)  y  9
2
2
Center: (4, 0) radius: 3
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
3. Write the standard equation of the circle. State the
center & radius.
4/2 = 2
2
2 =4
x  y  4 x  6 y  3  0 6/2 = 3
2
2
 x  4x
2
x
2
   y  6y
2
3
 4x  4   y  6 y  9  3  4  9
2
2
2
 x  2    y  3
 16
Center: (-2, 3) radius: 4
CASIMIRO A. YNARES SR. MNHS
2
3 =9
DIVISION OF RIZAL
4. Write the standard equation of the circle. State the
center & radius.
2 x  2 y  16 x  4 y  20  0
2
2
x  y  8 x  2 y  10  0
2
x
x
2
2
2
y
 8x
2
 2y
  10
 8 x  16    y  2 y  1  10  16  1
 x  4
2
2
  y  1  7
2
Center : (4, 1) Radius : 7  2.6
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
Write the general form of the equation of the circle.
 x  4
2
  y  3  36
2
Square of Binomial
x  8 x  16  y  6 y  9  36
2
2
x  8 x  16  y  6 y  9  36  0
2
2
x  y  8 x  6 y  11  0
2
2
CASIMIRO A. YNARES SR. MNHS
DIVISION OF RIZAL
Solve the following:
A.) Distance between 2 points
1. What is the distance between point M (2, 3 ) and P( 5 , 6 )
2. What is the distance of the two coordinates ( -6, 8 )and( 0, 0 )
B.) Center-Radius of the Circle
1.) Find the equation if C( 2, 5) , r = 4.
2.) Find the Center and radius if the equation is 𝑥 2 + (𝑦 − 3)2 = 16.
3.) Find the standard form of the general equation
𝑥 2 + 𝑦 2 + 8y + 7 = 0.
CASIMIRO A. YNARES SR. MNHS
Answers:
A.)
1.) 4.24
2.) 10
B.)
2
2
1.) (𝑥 − 2) + (𝑦 − 5) = 16
2.) C(0, 3) , r = 4
2
2
3.) 𝑥 + (𝑦 + 4) = 9