standard equation

1. JENNIFER P. LADDARAN
EQUATION
OF A CIRCLE

2. .
OBJECTIVES
02
03
04
Illustrate the standard equation of a circle;
Express the equation of a circle in standard form;
Determine the center of a circle given its
standard equation;
Apply the importance of equation of a circle in
solving a real-life situation.
01

3. ACTIVITY:
Guess the Word

4. ¿=¿
E_ _ _ _ _ _ _

5. ¿=¿
C_ _ _ _ _

6. ¿=¿
R_ _ _ _ _

7. ¿=¿
V_ _ _ _ _

8. ¿=¿
S_ _ _ _ _ _ _

9. STANDARD EQUATION OF A
CIRCLE

10. A circle with center at
the origin and a radius
of r units is x2
+ y2
=r2

11. A circle with center at
(h,k) and a radius of r
units is (x-h)2
+ (y-k)2
=r2

12. For example:
The radius is 4 and the center is at the origin.
x2
+y2
=r2
x2
+y2
=42
x2
+y2
=16
An equation of a circle is x2
+y2
=16

13. For example, the circle
shown has a center
(3,5) and radius 4.

14. Another examples:
1. Write the standard form of equation of a circle with
center at the origin and radius 5.
2.Write the standard form of equation of a circle with
center at the origin and radius 7.
3. Write the standard form of equation of a circle with
center at the origin and radius 4.

15. Another examples:
1. Write the standard form of equation of a circle with
center (2,1) and radius 3.
2.Write the standard form of equation of a circle with
center (4,-2) and radius 5.
3. Write the standard form of equation of a circle with
center (-5,-1) and radius 4.

16. Find the center and the radius of a circle given the
equation
The center and the radius of a circle can be found given
the equation. To do this, the given equation to its
standard form is the center of the circle is (h,k), or the
center of a circle is the origin. Once the center and the
radius of the circle found.

17. Example 1: Find the center and the radius of a circle
and draw its graph.
Example 2:Find the center and the radius of a circle
and draw its graph.

18. For example:
1. Determine the center and the radius of a circle
(x-2)2
+ (y-4)2
=25
2. Determine the center and the radius of a circle
(x-5)2
+ (y-6)2
=36.
3. Determine the center and the radius of a circle
(x-3)2
+ (y+3)2
=81.

19. A cellular phone networks uses towers to transmit calls. Each tower
transmits to circular area. On grid of a town, the coordinates of the
towers and the circular areas covered by the towers are shown.
Write the equations that represent the transmission boundaries of
the towers.

20. 5 The answer is correct with
complete solution.
4 The answer is correct with
incomplete solution
3 The answer is correct with
wrong solution
2 The answer is correct with
no solution
1 The answer is wrong with
solution
GROUP ACTIVITY
Direction: I will group you into 5 groups. I will provide 1/8
manila paper and a marker. Assign your team leader and a
presentor. I will score your output based on my scoring scale:

21. Group 1 – Write the equation of
a circle in standard form.
a. center (5,3) r=5
b. center (3,2) r=7
Group 4 – Write the equation of a circle
in standard form.
a. center (2,2) r=7
b. center (7,3) r=5
Group 2 – Determine the center and
the radius of a circle given the
equation.
a.
b.
Group 5- Determine the center
and the radius of a circle given
the equation.
1.
2.
Group 3- Determine the center
and the radius of a circle given the
equation.
1.
2.

22. If the statement is correct,
say FACT and if not say BLUFF

23. )
1.The x2
+y2
=r2
is the standard equation of a circle with
center at the origin.
2. The is the equation of a circle with center at (2,3) and
radius of 4
3. The center of the equation of a circle is (-5,8).
4. The is an example of a standard equation of a circle.
5. The (x-h)2
+(y-k)2
=r2
is the standard
equation of a circle with center at (h,k).

24. I. What are the
equations of a circle
written in standard
form?

25. II. Writing equations: Give the radius and coordinates of the center.
Write the equation of a circle in standard form.

26. III. Matching equations : Match each graph to its equation.
a.
b.
c.
02
01 03

27. IV. In 2 to 3 sentences, what is the
importance of equation of a circle
in solving real life situation.

28. ASSIGNMENT
FOLLOW UP: How does the equation of a
circle facilitate finding solutions to real-life
problems in making wise decision?
ADVANCED: Study about the general
equation of a circle.

29. Thank you