The acute angle between the lines $$\left(x^2+y^2\right) \sin \theta+2 x y=0$$ is

If the lines represented by $$(k^2+2) x^2+3 x y-6 y^2=0$$ are perpendicular to each other, then the values of $$\mathrm{K}$$ are

The equation of a line with slope $$-\frac{1}{\sqrt{2}}$$ and makes an intercept of $$2 \sqrt{2}$$ units on negative direction of $$y$$-axis is

If the lines respresented by $$a x^2-b x y-y^2=0$$ make angle $$\alpha$$ and $$\beta$$ with the positive direction of $$\mathrm{X}$$-axis, then $$\tan (\alpha+\beta)=$$