The correct option is B (32,−1)
Now PQ is the chord of contact of the tangents from the origin to the circle x2+y2−6x+4y+8=0→(1)
Equation of PQ is 3x−2y−8=0→(2)
Equation of a circle passing through the intersection of (1) and (2) is
x2+y2−6x+4y+8+λ(3x−2y−8)=0→(3)
if this represents the circumcircle of the triangle OAB, it passes through O(0, 0), so λ=1 and the equation (3) becomes x2+y2−3x+2y=0
∴ The required coordinates of the centre are (32,−1)