What does a "sonic boom" have to do with hyperbolas?

sonicboomplane_navy.jpg

The Whisper Room

What does this have to do with ellipses?

ab

ca F1F2b

A1A 2

B1

B

The Pythagorean Property

b2 c2 a2+ =

b2c2 a2-=

Vertical EllipseHorizontal Ellipse

Horizontal Ellipse Vertical Ellipse

Sketch each ellipse. Identify the length of the major and minor axes, the coordinates of the center, foci and vertices.

Constant

BY SYMMETRY

FOCAL RADII PROPERTY

Sketch each ellipse. Identify the length of the major and minor axes, the coordinates of the center, foci and vertices.

From Standard Form to General Form and Back Again ...

Standard Form

General Form

Standard Form

Generating Hyperbolas HOMEWORK