standard-form-of-the-eq.-of-the-circle.pptx

Performance in Mathematics 9 reflects students' understanding of algebra, geometry, and basic statistics. It indicates their ability to solve problems, apply mathematical concepts, and think logically. Strong performance demonstrates mastery of key skills, while poor performance may highlight gaps in foundational knowledge that require targeted intervention and support.

1. Learning Competencies The learners define a circle (STEM_PC11AG-Ia-2) The learners determine the standard form of the equation of the circle (STEM_PC11AG-Ia-3)

2. Math Prayer Dear Lord, we thank you for the wide range of opportunities and blessings You graphed for us. Forgive us, for the times when our doings fail to be parallel and not even coinciding to Your will. With You as the center and domain of our activities, it is surely that all our negative conditions will be inversed. Fill in with grace the hollow points in the line of our lives. Help us to be consistent of our actions. May they be bound inside Your never ending plane of goodness and be ways to fulfill our function which is to increase the circumference of the circle of Your love.

3. ACTIVITY No.1 FOLLOW THE INSTRUCTIONS

4. 1. Draw a circle .

5. 2. Name the circle as circle A .

6. 3. Draw a radius ( )  

7. 4. Draw a diameter ( ).  

8. 5. Draw a tangent line tangent to point C .

9. RUBRICS: Accuracy – 10 Neatness – 5 Organization – 5 Total - 20

10. ANALYSIS 1. How are you going to define a radius? 2. What is the relationship of radius to the diameter? 3. What is the relationship of tangent line to the radius of the circle?

11. Circle and It’s Standard Form

12. OBJECTIVES: A. Define a circle. B. Determine the standard form and general form of the equation of the circle. C. Recognize the importance of teamwork in the group activity.

13. A circle is the locus of all points in the plane having the same fixed positive distance, called the radius, from a fixed point, called the center .

14. Equation of a circle in standard form. An equation of a circle whose center is at ( h,k ) and radius is r > 0 is: (x – h) 2 + (y – k) 2 = r 2 .

15. In each item, give the standard equation of the circle satisfying the given conditions. (1) center at the origin, radius 4 (2) center (−4,3), radius √7 (3) center (5,−6), tangent to the y-axis (4) center (5,−6), tangent to the x-axis (5) It has a diameter with endpoints A(−1, 4) and B (4,2)

16. General Form of the Equation of the Circle. The students are going to expand the standard form of the equation of a circle. If the equation of a circle is given in the general form Ax 2 + Ay 2 + Cx + Dy + E = 0, A 0, or x 2 + y 2 + Cx + Dy + E = 0, we can determine the standard form by completing the square in both variables .  

17. Determine the standard form of the equation of a circle given the general form. (1) x 2 + y 2 −6x = 7 (2) x 2 + y 2 −14x + 2y = − 14

18. Determine the general form of the equation of a circle. (1) center at the origin, radius 4 (2) center (−4,3), radius √7

19. Working Individually Find the standard form and general form of the equation of the circle with the following conditions: 1. Center is at C(2,-5) and radius is 3. 2. Has a diameter whose endpoints are the points A(3,4) and B(-3,12)

20. Trip Around Tanza

21. Rubrics: Accuracy – 10 Neatness – 5 Organization – 5 Total 20

22. Mulawin Station Center (6, -5), radius 11

23. Sanja Mayor Station Diameter with endpoints (-1,3) and (9,1 )

24. Biga Station Center (5,7) tangent to the x – axis

25. Punta Station Center (-4,9) tangent to y-axis

26. Guide Questions: 1. What is a circle? 2. What is the standard form of the equation of the circle? 3. What is the general form of the equation of the circle?

27. SW#2 Determine the equation of the circle with the following conditions: 1. Center at the origin, radius 4 2. Center at (2, -1), radius 3 3. Center at (-3,5), diameter 10.

28. ASSIGNMENT; Determine the equation of the circle with the following condition: Center (2,1), through (8, - 3)