Navigation A lighthouse is on an island 3 miles from a long, straight shoreline. A boat sails around the island; deliberately following a path that always keeps it twice as far from the shoreline as it is from the lighthouse. What is an equation of the conic section describing the boat's path?
Draw a diagram of the situation with the lighthouse at (0, 0), the shore at the line
The distance from the boat to the lighthouse is
This is the standard-form equation for a horizontal ellipse centered at
The boat follows an elliptical path modeled by the equation