A circle of radius `2` lies in the first quadrant and touches both the axes. Find the equation of the circle with centre at `(6,5)` and touching the above circle externally.

Explanation

`C_1(2,2),r_1=2`

`C_2(6,5),r_2=?`

`C_1C_2=r_1+r_2`

`sqrt((6-2)^2+(5-2)^2)=2+r_2`

`sqrt(16+9)=sqrt25=2+r_2`

`r_2=5`

`(x-6)^2(y-5)^2=25`.