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# Pre-Cal 40S Slides December 13, 2007

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More on the ellipse.

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### Pre-Cal 40S Slides December 13, 2007

1. 1. The Whisper Room What does this have to do with ellipses?
2. 2. The Anatomy of The Ellipse B1 P b a a A1 A2 c O c F1 F2 b B2 O is the CENTRE
3. 3. 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
4. 4. Vertical Ellipse Horizontal Ellipse
5. 5. FOCAL RADII PROPERTY Constant BY SYMMETRY
6. 6. Sketch each ellipse. Identify the length of the major and minor axes, the coordinates of the center, foci and vertices.
7. 7. Sketch each ellipse. Identify the length of the major and minor axes, the coordinates of the center, foci and vertices.
8. 8. 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.
9. 9. 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.