f the tangent at the point P on the circle  x2+y2+6x+6y=2 meets the straight line 5x−2y+6=0 at a point Q on the y-axis, then the length of PQ, is

The line 5x−2y+6=0 cuts y-axis at at Q(0,3). Clearly, PQ  is the length of the tangent drawn from Q on the circlex2+y2+6x+6y−2=0∴ PQ=0+9+6×0+6×3−2¯=5