Question

addison and kelsey are running on a path modeled by x^2+y^2-10x-18y-378=0, where the distance is in meters. what is the maximum distance between the runners at any given time

Answer 1

The maximum distance is the diameter of the circle, which is of 44 units.

The equation of a circle of radius r and center $(x_0,y_0)$ is given by:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

• 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:

$x^2 + y^2 - 10x - 18y - 378 = 0$

We complete the squares to place it in the standard format, thus:

$x^2 - 10x + y^2 - 18y = 378$

$(x - 5)^2 + (y - 9)^2 = 378 + 25 + 81$

$(x - 5)^2 + (y - 9)^2 = 484$

Thus, the radius is:

$r^2 = 484 \rightarrow r = \sqrt{484} = 22$

Then, the diameter is:

$d = 2r = 2(22) = 44$

The maximum distance is the diameter of the circle, which is of 44 units.

A similar problem is given at brainly.com/question/24992361