The Whisper Room

What does this have to do with ellipses?

b

c

a

F1F2b

A1A2

B1

B2

Oa

c

The Anatomy of The Ellipse

O is the CENTRE

P

ab

ca F1F2b

A1A2

B1

B

The Pythagorean Property

b2 c2 a2+ =

b2c2 a2 -=

Vertical EllipseHorizontal Ellipse

Horizontal Ellipse Vertical Ellipse

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.

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

A parabola has vertex (0, 0) and focus on a coordinate axis. Write the equation of the parabola if:

(b) the directrix is defined by the line y = 8.

(a) the focus is: (i) (4, 0) (ii) (-6, 0) (iii) (0, 3)

For each ellipse whose equation is given below

(i) Write the equation in standard form(ii) Determine the lengths of the major and minor axes, the coordinates

of the verticies, and the coordinates of the foci.(iii) Sketch a graph of the ellipse.