Question

A lighthouse is located at (1, 2) in a coordinate system measured in miles. A sailboat starts at (–7, 8) and sails in a positive x-direction along a path that can be modeled by a quadratic function with a vertex at (2, –6). Which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse?

Answer 1

second answer

Explanation:

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Answer 2

For the answer to the question above, The first equation in each set of equations is an equation of a circle. Since you want to know if the sailboat comes within 5 miles of the point (1,2), the radius of the circle will be 5. The equation of a circle shows that the radius is squared. So 5 squared is 25. So answers two and four look good so far. Next, you are given the vertex, (h,k) as (2,-6). So looking at the equation of a parabola, we are looking for an answer with a k value of -6. Answer four has a k value of 8, however, answer two has a k value of -6.