A parabola touches the lines y= x and y=-x at P (3, 3) and Q (2,-2) respectively. Then 

 Midpoint of PQ=$(\frac{5}{2},\frac{1}{2})$  =R
Slope of OR= $\frac{1}{5}$
Slope of axis =    $\frac{1}{5}$
($\therefore$  Line joining the point of intersection of tangents at A and B on parabola and mid-point of chord AB is always parallel to axis of parabola)
$\Rightarrow$  Slope of directrix = -5
Eq.of directrix:  y=-5x $\Rightarrow$  5x+y=0
Circle with OP as diameter:  $x^2+y^2-3x-3y=0$
Circle with OQ as diameter:  $x^2+y^2-2x+2y=0$
Focus is the point of intersection of circles:  $S=(\frac{30}{13},\frac{-6}{13})$
Eq.of line joining origin to focus is: x+5y=0