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

Homework Questions

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

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

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