Graphing Circle and how to find the center and radius of the circle

1. Topic2:
Topic Outline:
• define a circle.
• determine the standard form of
equation of a circle.
• graph a circle in a rectangular
coordinate system

2. Review

3. Activity
1.
2.
3.
6.
4
.
5.
7.
8.
9.
• Circumferenc
e
• Diameter
• Arc
• Tangent
• Sector
• Radius
• Secant
• Segment
• Chord

4. Basic Parts of a Circle
 Radius is the constant distance (segment
connecting the center and any point on
the circle.
 Center is the fixed point equidistant from
any point of the circle.
 Diameter is the longest chord of a circle,
connecting any two points of a circle and
passing through the center.

5.  Chord is the segment connecting any two
points of a circle.
 Tangent line is a line that touches the
circle at exactly one point called the
point of tangency.
 Secant line is a line that intersects the
circle at two points.

6. Definition of a
Circle
A circle is the set of all
points equidistant from
a fixed point called the
center. The distance
from the center of the
circle to any point on
the circle is called
theradius, denoted byr.

7. Definition of a
Circle
A circle is a type of conics
that can be formed when
the intersecting plane has
an angle of 90 degrees or
perpendicular to the axis
of the cone.

8. Figure 1: Circle with center at origin (0,0)
Figure 2: Circle with center not at origin
denoted by C(h,k)

9. STANDARD FORM OF THE EQUATION OF
A CIRCLE
Center at (h,k)
To solve for r, use distance formula:
r =
=
𝒓𝟐
=(𝒙 − 𝒉)𝟐
+(𝒚 −𝒌)𝟐

10. STANDARD FORM OF THE EQUATION OF
A CIRCLE
Center not at origin(h,k)
( 𝒙 − 𝒉)𝟐
+( 𝒚 −𝒌)𝟐
¿ 𝒓 𝟐
Center at origin (0,0)
𝒙 𝟐
+ 𝒚 𝟐
¿ 𝒓 𝟐

11. Example 1
If a circle has a center at (2, 3) and a radius of 4, what is the
equation of the circle?
( 𝒙 − 𝒉)𝟐
+( 𝒚 − 𝒌)𝟐
¿ 𝒓 𝟐
( 𝒙 − 𝟐)𝟐
+( 𝒚 − 𝟑)𝟐
¿ 𝟒𝟐
( 𝒙 − 𝟐)𝟐
+( 𝒚 − 𝟑)𝟐
=𝟏𝟔

12. Example 2
If a circle has a center at (0, -3) and a radius of 6, what is the
equation of the circle?
( 𝒙 − 𝟎)
𝟐
+[ 𝒚 − ( −𝟑 ) ]
𝟐
¿ (𝟔)
𝟐
𝒙 𝟐
+( 𝒚 +𝟑 )𝟐
= 𝟑𝟔
( 𝒙 − 𝒉)𝟐
+( 𝒚 −𝒌)𝟐
¿ 𝒓 𝟐

13. Example 3
What is the equation of the circle whose center is at the origin and
radius is 9.
𝒙 𝟐
+ 𝒚 𝟐
¿ 𝒓 𝟐
𝒙 𝟐
+ 𝒚 𝟐
¿ (𝟗 )𝟐
𝒙 𝟐
+ 𝒚 𝟐
=𝟖𝟏

14. Example 4
Given the equation of the circle what is the coordinate of the center and the radius?
Center:
C (h,k)
C (-1,-6)
Radius:
𝑟2
=25
√𝑟2
=√25
r

15. Example 5
Given the equation of the circle what is the coordinate of the center and the radius?
𝑥2
+( 𝑦 − 2)2
=49
Center:
C (h,k)
C (0,2)
Radius: 𝑟2
=56
√𝑟2
=√56
√𝑟
2
=√4 ∙14
𝑟 =2 √14