Respuesta :
The maximum distance between them is the diameter of the circle, which is of 44 units.
The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The diameter is twice the radius, and is the maximum distance between two points on the same circle.
They are running on a circular path, modeled by:
[tex]x^2 + y^2 - 10x - 18y = 378[/tex]
Completing the squares, the equation is:
[tex](x - 5)^2 + (y - 9)^2 = 378 + 5^2 + 9^2[/tex]
[tex](x - 5)^2 + (y - 9)^2 = 378 + 25 + 81[/tex]
[tex](x - 5)^2 + (y - 9)^2 = 484[/tex]
Then, the radius is: [tex]\sqrt{484} = 22[/tex], which means that the maximum distance between the runners at any given time is of 44 units.
A similar problem is given at https://brainly.com/question/25008198
