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Question 470340: The City’s Parks and Recreation Department has called the Algebra Society to help them design the new gardens that they will be developing in the west end of town. For the gardens, they have purchased a rectangular lot that is 42 feet wide and 87 feet long. The most important aspect of the new garden will be an elliptical walkway. In the center of the ellipse will be a grand fountain, and two smaller fountains are planned at the foci of the ellipse. The radius of the large fountain will be twice the radius of the smaller fountains. The centers of the small fountains will be the foci of the inner ellipse. The edge of the smaller fountains will be tangent(i.e. will touch) to the elliptical walkway. The Department provided the following sketch as a guide. The elliptical walkway will be 3 feet wide and tangent to a 3-foot walkway around the perimeter of the park.
Help the Department by finding the radius of the Grand Fountain and the radius of each smaller fountain.
Answer by ccs2011(207)   (Show Source):
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