Title: 10.2 Introduction to Conics: Parabola
110.2 Introduction to ConicsParabola
- General Equation of all Conics
- Latus rectum
2The General equation of all Conics
- Definition of a Conics
- conic - a curve generated by the intersection of
a plane and a circular cone -
3The 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
4Parabola
- 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.
5The Vertex of the Parabola
- The midpoint of a line segment between the Focus
and - the Directrix
6Equation of the Parabola
- Depend if the parabola open to the right / left
or Up and Down. - Up or Down Right / left
7Writing the equation of the Parabola
- Find the Vertex and a point on the parabola.
- What Equation to Use?
8Writing the equation of the Parabola
- Replace h,k, x and y.
- Vertex ( 1, -4)
- Point ( 0, -3)
- Need to solve for p.
9Writing the equation of the Parabola
- Replace h, k and p.
- Vertex ( 1, -4)
- Point ( 0, -3)
10Writing the equation of the Parabola
11The 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
12Find 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)
13Find 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)
14Find 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)
15Find 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)
16Find the equation of the Line tangent to the
parabola at a given point
17Find the equation of the Line tangent to the
parabola at a given point
- Point-slope form the line
18Find the equation of the Line tangent to the
parabola at a given point
- Point-slope form the line
19Homework
- Page 712 715
- 6, 12, 18, 24,
- 28, 34, 40, 44,
- 50, 56, 64, 70
20Homework
- Page 712 715
- 10, 20, 26, 42,
- 48, 58