The centre of the circle whose radius is 5 and which touches the circle `x^(2)+y^(2)-2x-4y-20=0` at `(5,5)` is

Options

A. `(10,5)`
B. `(5,8)`
C. `(5,10)`
D. `(9,8)`

Answer

D

Explanation

The centre and radius of given circle
`x^(2)+y^(2)-2x-4y-20=0` are `C_(1)(1,2) and r=sqrt(1^(2)+2^(2)+20)=5`
Since, the radii of the circles are equal, therefore the two circles will touch externally and the point of contact will be the mid-point between two centres.
Let coordinates of the centre of required circle be (h, k).
`therefore (h+1)/(2)=5 and (k+2)/(2)=5 rArr h=9`
and k = 8
Hence, centre of the circle is (9, 8).