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ahmedelshfie
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 « Embed this message on: May 21, 2010, 12:52:48 am »

This following applet is The area of an ellipse
Created by prof Hwang Modified by Ahmed
Original project The area of an ellipse

The area of an ellipse with semimajor axis a and semiminor axis b is $A_e=\pi a b$
You will find area of a circle A_c is the projection of area of an ellipse A_e.
And $A_c =A_e \cos\theta$
Because $a=b*\cos\theta$ and the area of circle with radius $a$ is $A_c=\pi a^2$
Since $A_e \cos \theta =\pi a^2, A_e= \pi a^2/\cos\theta=\pi a \frac{a}{\cos\theta}=\pi a b$

You can drag the slider to change the length of semimajor axis of the ellipse so the maximum height is $2*Z$

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