The range of g so that we have always a chord of contact of tangents drawn from a real point  ( a , a)  to the circle  x2+y2+2gx+4y+2=0, is

For a real chord of contact of tangents drawn from (α,α) to the circle x2+y2+2gx+4y+2=0 the point  (α,α)must lie outside the circle. ∴    α2+α2+2gα+4α+2>0⇒    α2+gα+(2α+1)>0⇒    α2+(g+2)α+1>0Since a assumes real values. Therefore, (g+2)2−4>0⇒ g2+4g>0⇒−4