Semi Detailed LP

SEMI-DETAILED LESSON PLAN Mathematics for Grade 10 I. OBJECTIVES At the end of the discussion, 85% of the students should be able to: 1. Identify the radius and center of a circle given its equation 2. Compute for the equation of a circle given the center and the radius 3. Differentiate the standard and general form of the equation of the circle II. SUBJECT MATTER TOPIC: REFERENCES: MATERIALS: TIME:

Determining the center and radius of a circle given its equation and vice versa Geometry III. 2013. pp. 250-252 BEAM III – Module 22: Equation of a Circle projector and laptop 30 minutes

III. PROCEDURE (4As) Daily Routine Teacher tells students to stand up and pray and ask them to clean up and remove the unnecessary things under the desks. After which, the teacher greets the students a good morning. Preparatory Activities Review The teacher asks the students to have a recap of the previous lesson. Motivation Let the students describe the image below.

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Based from the students’ responses, introduce the lesson for the day and the lesson objectives. A. Activity  Divide the class into two then ask for a representative from each group while the rest of the class shall perform the same task that will be given in their respective seats.  Let them draw a Cartesian Coordinate Plane then plot A(2,2). Ask them to draw point B where B is a moving point at a distance 3 from point A.

B. Analysis  Let the students identify the figure that they have formed from their drawings.  Using the given information upon the teacher’s guidance let the students identify the center and the radius of a circle.  Emphasize the relationship between the radius and the circle, and how it is formed. C. Abstraction  Introduce the two forms of the equation of a circle: o STANDARD FORM: (𝑥 − ℎ)2 + (𝑦 − 𝑘)2 = 𝑟 2 where: (h, k) is the center of the circle r is the radius of the circle o GENERAL FORM: 𝑥 2 + 𝑦 2 + 𝐴𝑥 + 𝐵𝑦 + 𝐶 = 0  Using the Standard Form, the equation of a circle can be determined if the radius and center of the circle is given. o Write the equation of a circle whose center is (2,5) and radius 4. (h,k) = (2,5) r=4 (x - h)2 + (y – k)2 = r2 (x - 2)2 + (y – 5)2 = 42 (x - 2)2 + (y – 5)2 = 16  Equation of the circle in standard form o The equation of a circle in standard form can be expressed in general form when it is expanded. Taking the latter as an example: (x - 2)2 + (y – 5)2 = 16 (x2-4x+4) + (y2-10y+25) = 16 x2 - 4x + 4 + y2 - 10y + 25 -16 = 0 x2 + y2 – 4x – 10y + 13 = 0  Equation of the circle in general form  On the contrary, the radius and center of a circle can be determined given the general equation of the circle.

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Find the center and the radius of a circle with the equation x2 + y2 – 6x – 8y + 21 = 0 x2 + y2 – 6x – 8y + 21 = 0 x2 + y2 – 6x – 8y = -21 (x2 – 6x + 9) + (y2 – 8y + 16) = -21 +9 + 16  By completing the square (x – 3)2 + (y – 4)2 = 4  Equation of the circle in standard form Therefore (h, k) = (3, 4) and r=2

D. Application  Board work o Write the equation of a circle whose center is in the point (2, 3) and contains the point (6, 6). o The end points of a diameter of a circle are (-6, 2) and (6, -2). Find its center & radius, and write the equation. o Determine the center and radius of the circle with the equation, 2𝑥 2 + 2𝑦 2 − 8𝑥 + 12𝑦 − 6 = 0 IV. EVALUATION 1. Solve for the equation of a circle with center at (1, 2) and radius 3. 2. Determine the center and radius of a circle whose equation is 𝑥 2 + 𝑦 2 + 10𝑥 − 4𝑦 + 25 = 0 V. ASSIGNMENT In a one half crosswise of a paper, graph the following equations: 1. (x - 2)2 + (y – 5)2 = 16 2. x2 + y2 – 6x – 8y + 21 = 0 Prepared by: Melissa Joy B. Feliciano BSED Math 3