10.2 Introduction to Conics: Parabola

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10.2 Introduction to ConicsParabola

• General Equation of all Conics
• Latus rectum

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The General equation of all Conics

• Definition of a Conics
• conic - a curve generated by the intersection of
  a plane and a circular cone

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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

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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.

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The Vertex of the Parabola

• The midpoint of a line segment between the Focus
  and
• the Directrix

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Equation of the Parabola

• Depend if the parabola open to the right / left
  or Up and Down.
• Up or Down Right / left

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Writing the equation of the Parabola

• Find the Vertex and a point on the parabola.
• What Equation to Use?

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Writing the equation of the Parabola

• Replace h,k, x and y.
• Vertex ( 1, -4)
• Point ( 0, -3)
• Need to solve for p.

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Writing the equation of the Parabola

• Replace h, k and p.
• Vertex ( 1, -4)
• Point ( 0, -3)

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Writing the equation of the Parabola

• Replace h, k and p.

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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

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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)

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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)

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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)

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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)

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Find the equation of the Line tangent to the
parabola at a given point

• Slope m

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Find the equation of the Line tangent to the
parabola at a given point

• Point-slope form the line

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Find the equation of the Line tangent to the
parabola at a given point

• Point-slope form the line

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Homework

• Page 712 715
• 6, 12, 18, 24,
• 28, 34, 40, 44,
• 50, 56, 64, 70

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Homework

• Page 712 715
• 10, 20, 26, 42,
• 48, 58