More on the ellipse.

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

3. The Anatomy of The Ellipse
B1 P
b
a a
A1
A2 c O c F1
F2
b
B2
O is the CENTRE

4. The Pythagorean Property B1
a
b
A1
A2 a c F1
F2
b 2
c2 = a 2
b+
B
2
c = a 2 - b2
Vertical Ellipse
Horizontal Ellipse

5. Vertical Ellipse
Horizontal Ellipse

6. FOCAL RADII PROPERTY Constant
BY SYMMETRY

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

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

10. A parabola has vertex (0, 0) and focus on a coordinate axis. Write the
equation of the parabola if:
(a) the focus is: (i) (4, 0) (ii) (-6, 0) (iii) (0, 3)
(b) the directrix is defined by the line y = 8.

11. 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.