In the interactive picture below, triangle ABC sits with two of its vertices along the x- and y-axes. Drag vertex A of the triangle. Notice that point A slides along the x-axis while point B slides along the y-axis. What curve do C and D (its reflection through the origin) seem to trace? You can change the lengths of the triangle by dragging the endpoints of the segments in the upper left corner. To clear the trace, click on the red 'X' in the lower right corner.
For every ellipse you draw, observe how the curve is circumscribed by the rectangle (Note: the trace of point A appears as individual red circles. As these circles are somewhat large, the trace may appear to sit slightly outside the rectangle).
Draw several ellipses. For each new one, just change the length of AB. Keep CB and AC the same. You'll see that each ellipse is circumscribed by the same rectangle.
The rectangle was constructed with lengths of 2CB and 2AC. Can you explain why these lengths do the trick? How can you circumscribe a whole family of ellipses into a rectangle with dimensions 14 x 8 feet?
The rectangle construction was suggested by David Dennis.