`f(x , y)=x^2+y^2+2a x+2b y+c=0` represents a circle. If `f(x ,0)=0` has equal roots, each being `2,` and `f(0,y)=0` has 2 and 3 as its roots, then the center of the circle is (a) `(2,5/2)` (b) Data is not sufficient (c) `(-2,-5/2)` (d) Data is inconsistent

Options

A. `(2,5//2)`
B. Data are not sufficient
C. `(-2,-5//2)`
D. Data are inconsistent.

Explanation

`x^(2)+2ax+c=(x-2)^(2)`
or `-2a=4,c=4`
or `a= -2,c=4`
`y^(2)+2by+c=(y-2)(y-3)`
or `-2b=5,c=6`
or `b=- (5)/(2),c=6`
Clearly, the data are not consistent.