The joint equation of pair of lines through the origin and having slopes $$(1+\sqrt{2})$$ and $$\frac{1}{(1+\sqrt{2})}$$ is

If $$4 a b=3 h^2$$, then the ratio of slopes of the lines represented by $$a x^2+2 h x y+b y^2=0$$ is

The distance between the lines $$3 x+4 y=9$$ and $$6 x+8 y=15$$ is

If the slopes of the lines given by the equation $$a x^2+2 h x y+b y^2=0$$ are in the ratio $$5: 3$$, then the ratio $$h^2: a b=$$