Question

Who wants a medal? :D...Anyone?

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

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 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.

So answer two must be the correct answer.

Answer 2

Thank you so much. (especially for the easy to understand explanation.