Lesson-3Graphing-a-circle.pptx Graphing a circle means plotting all the points that are the same distance from a fixed point called the center.

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Graphing a circle means plotting all the points that are the same distance from a fixed point called the center. Using its equation , we can find the center and the radius , then draw the circle on the coordinate plane.

1. PRE calculus AMADO R. GUMANGAN TEACHER III

2. Opening Prayer Heavenly Father, We come to you today in prayer, asking for your guidance and wisdom as we begin our class. Help us to stay focused and attentive as we learn and grow together. Give us the strength to stay motivated and the courage to ask questions when needed. this we ask, in jesus name, amen.

3. INTRODUCTION I n the previous lesson, you have known that we can write the equation of a circle given its graph, with its center and radius. What about if we reverse the situation? That is, the equation of the circle is given, we find its center and radius, then graph the circle

4. content / lesson GRAPHING CIRCLE AND FINDING THE CENTER AND THE RADUIS

5. Identify the center and the radius Example 1. Find the center and radius of the circle then graph. 𝑥² + 𝑦² − 2𝑥 − 3 = 0

6. Sketch the graph . Example 1. Find the center and radius of the circle then graph. 𝑥² + 𝑦² − 2𝑥 − 3 = 0 Solution: Rewrite, grouping together terms with the same variable 𝑥² − 2𝑥 + 𝑦² = 3 Completing the square for x. (𝑥² − 2𝑥 + 1) + 𝑦² = 3 + 1 (𝑥 − 1)² + 𝑦²= 4 (𝑥 − 1)² + 𝑦² = 2² So, C(1,0), r = 2.

7. graph

8. Graph the Circle Example 2. Graph the circle 𝑥² + 𝑦²− 6𝑥 + 4𝑦 + 4 = 0 Solution: Rewrite and group together terms with the same variable (𝑥² − 6𝑥) + (𝑦² + 4𝑦) = −4 Complete the square for x and y (𝑥² − 6𝑥 + 9) + (𝑦² + 4𝑦 + 4) = −4 + 9 + 4 (𝑥 − 3)² + (𝑦 + 2)² = 9 (𝑥 − 3)² + (𝑦 + 2) = 3² Hence, C(3,-2), r = 3. The graph is shown in Figure 2.

9. Activity 3. sketch me! 1. C(4, 0), r =3 2. C(-1,3), r = 2 3. C(3,-2), r = 5 4. C(0,-4), r = 1 5. C(-5,-2), r = 3  

10. Activity 4. graph the circles illustrated by the following equations   Equations A.x² + y² + 2x – 6y + 1 = 0 B. x²+ y² – 8x + 12 = 0 C. x² + y² + 8x + 15 = 0 D. x² + y² – 6x + 4y -12 = 0 E. x² + y² + 10x + 4y + 20 = 0  

11. LET’S PRACTICE! Find the center and radius of the circle. Then graph the circle problems involving extreme values . The Ay writing the teacher will start the lesson by writing the word “TANGENT LINE” on the bond asking the class what they know about a tangent line or where they first heard the word “ “TANGENT LINE” on the board and asking the class what they know about a tangent line or where they first heard the word “tangent”. LET’S PRACTICE! Find the center and radius of the circle. Then graph the circle. 1. 𝑥² + 𝑦² – 6𝑥 − 7 = 0 2. 𝑥² + 𝑦² + 8𝑥 + 12𝑦 + 3 = 0 3. 3𝑥² + 3𝑦² + 12𝑦 − 15 = 0 4. 𝑥² + 𝑦² − 12𝑥 – 6𝑦 – 4 = 0 5. 𝑥² + 𝑦² + 10𝑥 – 12𝑦 = 3

12. practical application of concepts and skills in daily living . The Ay writing tstart the lesson by writing the word “TANGENT LINE” on the bond asking the class what they know about a tangent line or where they first heard the word “ “TANGENT LINE” on the board and asking the class what they know about a tangent line or where they first heard the word “tangent”. There are numerous uses for circles in architecture, landscaping, graphics, infrastructure, transportation, and other fields. Some of them are as follows. Circles have contributed significantly to civilization. Just look at how the invention of the wheel transformed society and our methods of transportation.

13. Thank you Xer madz