The equation of a straight line passing through the point $(1, 2)$ and inclined at $45^{\circ}$ to the line $y = 2x + 1$ is

The equation of one of the straight lines which passes through the point $(1, 3)$ and makes an angle of $\tan^{-1}(\sqrt{2})$ with the straight line $y + 1 = 3\sqrt{2}x$ is:

$A$ line $L$ passing through the point $(2,0)$ makes an angle $60^{\circ}$ with the line $2x-y+3=0$. If $L$ makes an acute angle with the positive $X$-axis in the anticlockwise direction,then the $Y$-intercept of the line $L$ is:

The lines $p(p^2+1)x - y + q = 0$ and $(p^2+1)^2 x + (p^2+1)y + 2q = 0$ are perpendicular to a line $L$ for

The equation of a line making an angle $60^{\circ}$ with the line $x+y-3=0$ and passing through the point $(1,1)$ is

$A$ value of $k$ such that the straight lines $y-3kx+4=0$ and $(2k-1)x-(8k-1)y-6=0$ are perpendicular is