What does a \"sonic boom\"
have to do with hyperbolas?
sonicboomplane_navy.jpg

The Whisper Room
What does this have
to do with ellipses?

The Pythagorean Property
B1
a
b
A2 a A1
F2 c F1
b 2 2
b+ c = a2
B
2 2 2
c =a - b
Horizontal Ellipse Vertical 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.

FOCAL RADII PROPERTY
Constant
BY SYMMETRY

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