If two circles  $x^2+y^2-6x-6y+13=0$ and  $x^2+y^2-8y+9=0$ interesects at A and B. The focus of the parabola whose directrix is line AB and vertex at  $(0,0)$ is

Common chord of the given two circles   $S=0,\&S^1=0\Rightarrow 3x-y-2=0$
vertex $(0,0)$ is given
‘Z’ is foot of perpendicular $A=(0,0)$ of  on the directrix  $\Rightarrow Z=(\frac{3}{5},-\frac{1}{5}).$ Since A is the midpoint of  $SZ\Rightarrow focusS=(-\frac{3}{5},\frac{1}{5})$