The centre of the smallest circle touching the circles `x^2+ y^2-2y -3=0` and `x^2 +y^ 2-8x -18y +93= 0` is:

Options

A. (3,2)
B. (4,4)
C. (2,5)
D. (2,7)

Answer

3

Explanation

Circles
`S_(1) : x^(2)+y^(2)-2y-3=0` and
`S_(2) : x^(2)+y^(2)-8x-18y+93=0`
`C_(1) -= (0,1)` and `r_(1)=2`
`C_(2) -= (4,9)` and `r_(2)=2`
Since circles have same radius , centre `C_(3)` of the smallest circle is collinear with `C_(1)` and `C_(2)` and is midpoint of `C_(1)C_(2)`.
`:. C_(3) -= (2,5)`