A tour boat travels between two islands that are 12 miles apart (see figure). For each trip between the islands, there is enough fuel for a 20-mile trip.

(a) Explain why the region in which the boat can travel is bounded by an ellipse.
(b) Let (0, 0) represent the center of the ellipse. Find the coordinates of the center of each island.
(c) The boat travels from Island 1, past Island 2 to one vertex of the ellipse, and then to Island 2 (see figure). How many miles does the boat travel? Use your answer to find the coordinates of the vertex.
(d) Use the results of parts (b) and (c) to write an equation of the ellipse that bounds the region in which the boat can travel.

Transcribed Image Text:

Island 2 Island 1 -12 mi- Not drawn to scale