`t_(1),t_(2),t_(3)` are lengths of tangents drawn from a point (h,k) to the circles `x^(2)+y^(2)=4,x^(2)+y^(2)-4x=0andx^(2)+y^(2)-4y=0` respectively further, `t_(1)^(4)=t_(2)^(2)" "t_(3)^(2)+16`. Locus of the point (h,k) consist of a straight line `L_(1)` and a circle `C_(1)` passing through origin. A circle `C_(2)` , which is equal to circle `C_(1)` is drawn touching the line `L_(1)` and the circle `C_(1)` externally.
Equation of `C_(1)` is

Options

A. `x^(2)+y^(2)-x-y=0`
B. `x^(2)+y^(2)-2x+y=0`
C. `x^(2)+y^(2)-x+2y=0`
D. `x^(2)+y^(2)-2x-2y=0`

Answer

D