Pre-calculus_Conic Sections_Circles.pptx

Pre-calculus
conic sections
circle

1. Understanding Circles in Pre-Calculus Marlon L. Dacanay Mathematics Teacher Grade 11-STEM

2. "Mathematics is the language in which God has written the universe." - Galileo Galilei

3. Color Name! ACTIVITY 1: Chord Diameter Tangent Secant Radius Center

4. Color Name! ACTIVITY 1: Chord Diameter Tangent Secant Radius Center

5. Color Name! ACTIVITY 1: Chord Diameter Tangent Secant Radius Center

6. Color Name! ACTIVITY 1: Chord Diameter Tangent Secant Radius Center

7. Color Name! ACTIVITY 1: Chord Diameter Tangent Secant Radius Center

8. Color Name! ACTIVITY 1: Chord Diameter Tangent Secant Radius Center

9. Color Name! ACTIVITY 1: Chord Diameter Tangent Secant Radius Center

10. OBJECTIVES: Define a circle and write its equation in standard form. Derive and manipulate the standard form of the equation of a circle. Appreciate the significance of circles in mathematics and everyday life.

11. Define me! GROUP ACTIVITY:

12. Define me! GROUP ACTIVITY: A circle is point set equidistant of in a plane all points that center are the given from a called the.

13. Circle A circle is the set of all points in a plane that are equidistant from a given point called the center.

14. Standard Form of the Equation of a Circle (x - h)² + (y - k)² = r² where (h, k) is the center and r is the radius (h, k) r

15. Examples: 1: Circle with center at (0, 0) and radius 5: ( x -0) ² + ( y -0) ² = (5)² x² + y² = 25 2 . Circle with center at (3, -2) and radius 4: ( x - 3)² + [ y -(- 2 )] ² = (4)² ( x - 3)² + (y + 2)² = 16 (x - h)² + (y - k)² = r² x² + y² = r²

16. Examples: 3. Center: (0, 0), Radius : 4 (x - h)² + (y - k)² = r² (x-0²) + (y-0)² = (40) ² x² + y² = 16 4. Center: (2, -1), Radius : 3 (x - h)² + (y - k)² = r² (x-2²) + [y-(-1)]² = (3) ² (x - 2)² + (y + 1)² = 9 (x - h)² + (y - k)² = r²

17. Examples: 5. x² + (y - 3)² = 25 Center: (0, 3), Radius : 5 4. (x + 4)² + y² = 1 Center: (-4, 0), Radius : 1 5. (x - 1)² + (y - 1)² = 4 Center: (1, 1), Radius : 2 (x - h)² + (y - k)² = r²

18. Group Activity: Find My Equation!

19. Group Activity: Find My Equation! Group 1 Group 2

20. Understanding the properties and equations of circles is fundamental in geometry and has numerous applications in various fields. Importance: Circles are not just theoretical concepts but are widely used in engineering, astronomy, and everyday objects. Generalization

21. 1. Astronomy: The orbits of planets are often approximated as circles. 2. Engineering: Gears and pulleys are designed based on circular motion. Real-life Relation

22. Relating Across Discipline Physics: Understanding circular motion and centripetal force is crucial in physics, especially in mechanics. For instance, the principles of circular motion are applied when analyzing the forces acting on a car moving along a curved path.

23. Isaiah 40:22 (NIV): "He sits enthroned above the circle of the earth, and its people are like grasshoppers. He stretches out the heavens like a canopy, and spreads them out like a tent to live in."

24. Any question?