Question

A hiker is lost in the woods. A search team has created a coordinate grid to represent the woods. Each unit on the grid is one square mile. The hiker was last seen at (5, 10) and could have walked 12 miles in any direction since then. Which equation represents the area the hiker could be in?

Answer 1

Answer: The circle in the problem takes the form (x-h)^2+ (y-k)^2. The hiker started at the center of the circle (h,k)=(5,10). The radius of the circle = 12. When you plug these values into the equation, you get (x-5)^2+ (y-10)^2=12^2

Answer 2

Since the hiker can move in any direction, the equation that represent the area in which the hiker could be will be the equation of circle with radius r=12 and center (5,10)
The equation of a circle with radius r and center (h,k) is:

`(h-x) ^(2) +(y-k) ^(2) =r ^(2)`
The only thing we have left is replace the values to get:

`(x-5) ^(2) +(y-10) ^(2) =12 ^(2)`

`(x-5) ^(2) +(y-10) ^(2) =144`