ParabolaApplications

Mr. Bigham

Painted by Gieulio Parigi, ≈ 1600 A.D., Florence Italy

An Ancient Application of Parabolas

Archimede’s “Solar Death Ray”

Modern Solar Death Energy Rays

1. Circle2. Ellipse3. Parabola 4. Hyperbola

Conic Sections

Geometry:

Algebra:Ax2 + Bxy + Cy2 + Dx + Ey + F = 0

Parabola

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0

( B = 0, C = 0)

More Parabolas

Parabola anatomy

V

F = FocusV = VertexL = Directrix

Parabola property

Create your own

One way to construct a parabola

• Begin with paper, pencil, straight edge, and compass

• Make a horizontal line, this is your directrix• Make a point above the line, this is your focus• Mark a point on the directrix

Circles

Conic Sections