the circle of radius 2 unit lies in the first quadrant and touches both the axes of coordinates , equation of circle with centre (6,5) and touching the above circle externally is _______

Dear student,

the circle of radius 2 unit lies in the first quadrant and touches both the axes of coordinates
==> (x-2)^2 + (y-2)^2 = 2^2

Let equation of circle with centre (6,5) be
(x-6)^2 + (y-5)^2 = r^2

Now both the circles touch each other externally
So r1 +r2 = distance between the centers
from here you will get r