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10.2 Introduction to Conics: Parabola

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10.2 Introduction to Conics: Parabola General Equation of all Conics Latus rectum The General equation of all Conics Definition of a Conics conic - a curve generated ... – PowerPoint PPT presentation

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Title: 10.2 Introduction to Conics: Parabola


1
10.2 Introduction to ConicsParabola
  • 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
  • Ax2 Bxy Cy2 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 Down Right / 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
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