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 $$h^2: a b=$$

The equation of line, where length of the perpendicular segment from origin to the line is 4 and the inclination of this perpendicular segment with the positive direction of X-axis is 30$$^\circ$$, is

If two lines represented by $$a x^2+2 h x y+b y^2=0$$ makes angles $$\alpha$$ and $$\beta$$ with positive direction of $$\mathrm{X}$$-axis, then $$\tan (\alpha+\beta)=$$