Respuesta :
The maximum distance is the diameter of the circle, which is of 44 units.
The equation of a circle of radius r and center [tex](x_0,y_0)[/tex] 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 inside a circle.
In this problem, the circular path is modeled by:
[tex]x^2 + y^2 - 10x - 18y - 378 = 0[/tex]
We complete the squares to place it in the standard format, thus:
[tex]x^2 - 10x + y^2 - 18y = 378[/tex]
[tex](x - 5)^2 + (y - 9)^2 = 378 + 25 + 81[/tex]
[tex](x - 5)^2 + (y - 9)^2 = 484[/tex]
Thus, the radius is:
[tex]r^2 = 484 \rightarrow r = \sqrt{484} = 22[/tex]
Then, the diameter is:
[tex]d = 2r = 2(22) = 44[/tex]
The maximum distance is the diameter of the circle, which is of 44 units.
A similar problem is given at https://brainly.com/question/24992361
