1. 10.2 Introduction to Conics: Parabola General Equation of all Conics Latus rectum

2. The General equation of all Conics Definition of a Conics conic - a curve generated by the intersection of a plane and a circular cone

3. The General equation of all Conics Definition of a Conics conic - a curve generated by the intersection of a plane and a circular cone Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0; Where A, B, C, D, E and F are all numbers

4. Parabola The curve formed by the set of points in a plane that are all equally distant from both a given line (called the directrix) and a given point (called the focus) that is not on the line.

5. The Vertex of the Parabola The midpoint of a line segment between the Focus and the Directrix

6. Equation of the Parabola Depend if the parabola open to the right / left or Up and Down. Up or DownRight / left

7. Writing the equation of the Parabola Find the Vertex and a point on the parabola. What Equation to Use?

8. Writing the equation of the Parabola Replace h,k, x and y. Vertex ( 1, -4) Point ( 0, -3) Need to solve for p.

9. Writing the equation of the Parabola Replace h, k and p. Vertex ( 1, -4) Point ( 0, -3)

10. Writing the equation of the Parabola Replace h, k and p.

11. The Chord touching the parabola and going through the center is called Latus rectum The Latus rectum goes through the Focus. The Latus rectum is 4 p

12. Find the equation of the Line tangent to the parabola at a given point Given point (3,3): Focus (0, 2) Equation (x - 0) 2 = 0.2(y – 1)

13. Find the equation of the Line tangent to the parabola at a given point Given point (3,3): Focus (0, 2) Equation (x - 0) 2 = 0.2(y – 1)

14. Find the equation of the Line tangent to the parabola at a given point Given point (3,3): Focus (0, 2) Equation (x - 0) 2 = 0.2(y – 1)

15. Find the equation of the Line tangent to the parabola at a given point Given point (3,3): Focus (0, 2) Equation (x - 0) 2 = 0.2(y – 1)

16. Find the equation of the Line tangent to the parabola at a given point Slope m =

17. Find the equation of the Line tangent to the parabola at a given point Point-slope form the line

18. Find the equation of the Line tangent to the parabola at a given point Point-slope form the line

19. Homework Page 712 – 715 # 6, 12, 18, 24, 28, 34, 40, 44, 50, 56, 64, 70

20. Homework Page 712 – 715 # 10, 20, 26, 42, 48, 58