If the two lines given by $$a x^2+2 h x y+b y^2=0$$ make inclinations $$\propto$$ and $$\beta$$, then $$\tan (\alpha+\beta)=$$

If the polar co-ordinates of a point are $$\left(\sqrt{2}, \frac{\pi}{4}\right)$$, then its Cartesian co-ordinates are

The equation of a line passing through $$(\mathrm{p} \cos \propto, \mathrm{p} \sin \propto)$$ ) and making an angle $$(90+\propto)$$ with positive direction of $$\mathrm{X}$$-axis is

The product of the perpendicular distances from $$(2,-1)$$ to the pair of lines $$2 x^2-5 x y+2 y^2=0$$ is