# 10.2 Introduction to Conics: Parabola - PowerPoint PPT Presentation

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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