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?
StartLayout Enlarged Left-Brace 1st Row (x minus 1) squared + (y minus 2) squared = 5 2nd Row y = StartFraction 14 Over 81 EndFraction (x minus 2) squared minus 6 EndLayout
StartLayout Enlarged Left-Brace 1st Row (x minus 1) squared + (y minus 2) squared = 25 2nd Row y = StartFraction 14 Over 81 EndFraction (x minus 2) squared minus 6 EndLayout
StartLayout Enlarged Left-Brace 1st Row (x minus 1) squared + (y minus 2) squared = 5 2nd Row y = Negative StartFraction 14 Over 81 EndFraction (x + 7) squared + 8 EndLayout
StartLayout Enlarged Left-Brace 1st Row (x minus 1) squared + (y minus 2) squared = 25 2nd Row y = Negative StartFraction 14 Over 81 EndFraction (x + 7) squared + 8 EndLayout

StartLayout Enlarged Left-Brace 1st Row (x minus 1) squared + (y minus 2) squared = 25 2nd Row y = StartFraction 14 Over 81 EndFraction (x minus 2) squared minus 6 EndLayout. Option B

This is further explained below.

What is a parabola?

a curve in an open plane that is symmetrical and open at both ends and created by the intersection of a cone with a plane that is parallel to the side of the cone. Under the influence of gravity, the route taken by a projectile takes the form of a curve similar to this one.

Generally, Every single pair of equations begins with an equation representing a circle as their initial problem.

Because you are interested in finding out whether the sailboat is within 5 miles of the coordinates (1,2), you will set the radius of the circle to 5.

The calculation for a circle reveals that the square of the radius should be used. In this case, the answer is 25. So far, it seems that answers two and four are correct.

Following this, the vertex will be shown to you as (h,k) (2,-6). When we look at the equation of a parabola, we want to find a solution that has a k value of -6, so our search begins there.

In conclusion, the system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse is

StartLayout Enlarged Left-Brace 1st Row (x minus 1) squared + (y minus 2) squared = 25 2nd Row y = StartFraction 14 Over 81 EndFraction (x minus 2) squared minus 6 EndLayout