Respuesta :
The maximum distance between the runners at any given time is 38 meters.
What is general form of equation of a circle?
"The general form of equation of circle is [tex]x^2 + y^2 + 2gx + 2fy + c = 0[/tex]."
here center = (-g, -f) and radius = [tex]\sqrt{g^{2} +f^{2} -c}[/tex]
What is the equation of circle?
The equation of the circle with center (h, k) and radius 'r' is, [tex](x-h)^2 + (y-k)^2 = r^2[/tex]
For given question,
Addison and Kelsey are running on a path modeled by [tex]x^2 + y^2 - 12x - 8y - 309 = 0[/tex]
This means, they are running on a circular path.
By completing the squares, the equation is:
[tex]\Rightarrow x^2 -12x + 36+ y^2 - 8y +16 = 309 + 36+16\\\\\Rightarrow (x-6)^2+(y-4)^2=361\\\\\Rightarrow (x-6)^2+(y-4)^2=19^2[/tex]
This equation represents the circle with center (6, 4) and radius = 19
The maximum distance between the runners is the diameter of the circle.
diameter = 2 × radius
diameter = 2 × 19
diameter = 38 meters
Therefore, the maximum distance between the runners at any given time is 38 meters.
Learn more about the general form of equation of circle here:
https://brainly.com/question/10165274
#SPJ2
