The equations of the lines passing through the point $(3,2)$ which make an angle of $45^{\circ}$ with the line $x-2y=3$ are

If $3x + 4y - 5 = 0$ and $4x + ky - 8 = 0$ are two parallel lines,find the value of $k$.

The angle between the line $x+y=3$ and the line joining the points $(1,1)$ and $(-3,4)$ is

The angle between the line joining the points $(1, -2)$ and $(3, 2)$ and the line $x + 2y - 7 = 0$ is

$A$ line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $L_1: 2x + y + 6 = 0$ and $L_2: 4x + 2y - p = 0, p > 0$,at the points $A$ and $B$,respectively. If $AB = \frac{9}{\sqrt{2}}$ and the foot of the perpendicular from the point $A$ on the line $L_2$ is $M$,then $\frac{AM}{BM}$ is equal to

Let the angle between the lines $x-2y+3=0$ and $kx-y+2=0$ be $45^{\circ}$. If $k_1, k_2$ $(k_1 > k_2)$ are two distinct real values of $k$,then $k_1-2=$