1. Presented by: Herminia R. Miralles Ismael Mathay Sr. High School
Equation of a Circle
Presented by:
Herminia R. Miralles
Ismael Mathay Sr. High School

2. Introduction:
Level: Third Year
Duration: 55mins
Mode: Group Work

3. Objectives: At the end of the lesson the students should be able to:
Name the Parts of a Circle
Determine relationships between Lines and Circles.
Write the Equation of a circle on a coordinate plane.

4. Observation:
Look around the classroom in your notebook write down all the things that are round and looks like a circle.
Compare the things you have observed by the observation that your classmate made.
Are there similar things you have listed compare to your classmate?
3. Discuss among yourself what is a circle?

5. Circles
A circle is the set of all points in a plane that are equidistant from a given point in the plane known as the center of the circle. Circle name by its center. What is the name of the circle in the figure? .P

6. Parts of a Circle
A radius is a segment from the center of the circle to a point on the circle. (CP)
A chord is a segment whose endpoints lie on the circle. (AB) C .P B A

7. Equation of Circles
Look at the graph of a circle in example #1 and example #2.
Example 1:  Circle with center (0,0), radius 4                
What is the difference between the two circles?
Example 2 :  Circle with center (2,-5), radius 3
Graph:
Graph

8. To write an Equation of a Circle
Using Center- radius form: If center is at the origin. X2 + Y2 = r2 where r is the radius. 1. What is the center and and radius of the circle? Center (0,0), r = What is the equation of given graph of the circle given in the figure? X2 + Y2 = 42 or X2 + Y2 = 16

9. 3. What is the center and radius given in the figure. 4
3. What is the center and radius given in the figure? What is the equation of a circle in the figure?

10. Answers: C ( 0,0), r = 5 X2 + Y2 = 52 or X2 + Y2 = 25

11. 5. Write the equation for the circle shown below if it is shifted 3 units to the right and 4 units up. What is the new center and radius? What did you noticed about the Center? Circle whose radius not at the center.
A shift of 3 units to the right and 4 units up places the center at the point (3, 4).  The radius of the circle can be seen from the graph to be 5.
Equation: 
( x-3)2 + ( y -4)2 = 25

12. Standard Equation of a circle
In general, an equation for a circle with center at (h,k) and radius of r units is
(x-h)2 + (y-k)2 = r2
more examples

13. Examples:
1. What is the equation of the circle pictured on the graph below?
Answer

14. Answer:
1. Since the radius of this this circle is at its center is (0,0) , this circle's equation is (X-O)² +(Y-O)² = 1² X² + Y² = 1

15. 2. Look at the graph below, can you express the equation of the circle in standard form?
Answer

16. Answer;
2.   Since the radius of this this circle is 1, and its center is (1,0), this circle's equation is (X-1)² +(Y-0)² = 1 ² (X-1)² + Y² = 1

17. Find the center by using the midpoint formula.
3.  Write the equation of a circle whose diameter has endpoints (4, -1) and
(-6, 7).
1. How do u get the center ?
Find the center by using the midpoint formula.   

18. Find the radius by using the distance formula.
2. How do you find the radius?
Find the radius by using the distance formula.
Points (-6,7) and (-1,3) were used here.  (d = distance, or radius)
Equation: (x+1)2 +(y-3)2 =√41

20. Exercises A. What is the radius of the circles
X2+Y2 =9
X2+Y2 =16
X2+Y2 =25
X2+Y2 =36
X2+Y2 =49

21. B. Radius of Circles 3 4 5 6 7

22. D. Write an equation of the figure given below.

23. C. Write an Equation of a circle given the following:
Center and Radius.
C(0,0), r = 12
C ( 0,0), r = 10
C ( 2, 3), r = 5
C ( -4, 6), r=9
C ( -2, -3), r = 8

24. Worksheet 2
Write about what you have learnt today and what do you gain from the topic discussed about Equation of a circle?
Prepare one last question you may want your classmates to answer regarding the lesson discussed.
Read and study about how to get an Equation of a circle using Standard Equation Form.

25. Assignment:
Read and study about how to get an Equation of a circle using standard form.