Clearly OQ is perpendicular to QP, and hence is the tangent at Q. Its polar equation is therefore .
And if the point of contact of the other tangent is T and the centre of the circle is C = (3, 1), then . So . You can easily find the sine of the angle between OC and the x-axis. So you can work out the angle between OT and the x-axis, and hence its polar equation.