If lines represented by $$\left(1+\sin ^2 \theta\right) x^2+2 h x y+2 \sin \theta y^2=0, \theta \in[0,2 \pi]$$ are perpendicular to each other then $\theta=$ ...........

If $(-\sqrt{2}, \sqrt{2})$ are cartesian co-ordinates of the point, then its polar co-ordinates are .........

The $y$-intercept of the line passing through $A(6,1)$ and perpendicular to the line $x-2 y=4$ is ...........

The joint equation of pair of straight lines passing through origin and having slopes $(1+\sqrt{2})$ and $\left(\frac{1}{1+\sqrt{2}}\right)$ is .......