The equation of the line passing through $(c, d)$ and parallel to $ax + by + c = 0$ is

If three points $(h, 0), (a, b),$ and $(0, k)$ lie on a line,show that $\frac{a}{h} + \frac{b}{k} = 1$.

$A$ line passing through the point $A(2, 3)$ makes an angle of $45^{\circ}$ with the $x$-axis and intersects the line $x + y + 1 = 0$ at point $P$. Find the distance $AP$.

Find the equation of a line which is bisected at the point $(x_1, y_1)$ by the axes.

The line $L_1$ passes through the points $(-1, 2)$ and $(3, 6)$. If $L_1$ divides the line $L_2$ (which passes through $(3, -1)$) in the ratio $1:3$ internally, and the point of intersection lies on $L_1$, find the equation of $L_2$ given that it is perpendicular to $L_1$.

Let $PS$ be the median of the triangle with vertices $P(2, 2)$,$Q(6, -1)$,and $R(7, 3)$. The equation of the line passing through $(1, -1)$ and parallel to $PS$ is