Question 5 • Advanced Algebra: Concepts and Connections
The points within 5 miles of the lighthouse form a circle centered at (1, 2), so its equation is (x − 1)² + (y − 2)² = 5² = 25. The boat’s path has vertex (2, −6), so write it as y = a(x − 2)² − 6. Substituting the starting point (−7, 8) gives 8 = 81a − 6, so a = 14/81. Thus the system in choice A is correct.
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