Focus and Directrix Notes
"Cause it's a long road to wisdom but it's a short one to being ignored."
~The Lumineers
Get ready for a HWQ!
Focus and Directrix Notes
OpenerOpenerFind the missing coordinate points for the
following shapes.
SquareRhombus(2a,8b)
(2a, 6b)
(a,8b)
(?,?)
(4,8)
(5,4)
(4,0)
(?,?)
Focus and Directrix Notes
Review:Review:axis of symmetry
Vertex (h,k)
vertex form:
axis of symmetryVertex (h,k)
Focus and Directrix Notes
Focus and Directrix of a Parabola
Focus: fixed point inside the parabola on the axis of symmetry
Directrix: line outside the parabola; perpendicular to the axis of symmetry
the focus and directrix are equidistant from the vertex
Focus and Directrix Notes
The ParabolaA parabola is the collection of all points P in the plane that are the same distance from a fixed point F as they are from a fixed line D.
Focus and Directrix Notes
Parabolas with vertex (h, k)(y k)2=4a(x h)
vertex:focus:directrix:axis of symmetry:
(y k)2 = 4a(x h)
vertex:focus:directrix:axis of symmetry:
Focus and Directrix Notes
Parabolas with vertex (h, k)vertex:focus:directrix:axis of symmetry:
vertex:focus:directrix:axis of symmetry:
(x h)2 = 4a(y k)
(x h)2 = 4a(y k)
Focus and Directrix Notes
Example One: Determine the 6 characteristics of
opens:vertex:focus:directrix:axis of symmetry:value of a:
Focus and Directrix Notes
Example Two: Determine the 6 characteristics of
opens:vertex:focus:directrix:axis of symmetry:value of a:
Focus and Directrix Notes
Example Three: Graph, identify the 6 characteristics, and write the equation of the parabola with vertex at (2, 3) and focus at (0, 3).
opens:vertex:focus:directrix:axis of symmetry:value of a:
Attachments
long_road.jpg&w=1105&h=737&ei=CKwjUZWrIsaE2QXpg4HgCQ&zoom=1.url