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.

Options

A. `x^(2) + y^(2) - 12x - 10y + 52 = 0`
B. `x^(2) + y^(2) - 12x - 10y + 12 = 0`
C. `x^(2) + y^(2) - 12x - 10 y - 52 = 0`
D. None of these

Answer

A

Explanation

Distance between `C_(1)` & `C_(2)`
`C_(1)C_(2) = 2 +r`
`sqrt((6-2)^(2) + (5-2)^(3)) = 2+r`
`5 = 2+r`
`rArr r = 3`
`:.` Equation of the required circle
`(x-6)^(2) + (y-5)^(2) = 3^(2)`