Find the equation of the line passing through $(-3, 5)$ and perpendicular to the line passing through the points $(2, 5)$ and $(-3, 6)$.

Find the equation of the line that bisects the line segment joining the points $(5, 3)$ and $(4, 4)$ and makes an angle of $45^{\circ}$ with the positive direction of the $x$-axis.

The equation of the line passing through $(4, -6)$ and making an angle of $45^\circ$ with the positive $x$-axis is:

$A$ ray of light coming from the point $(2, 2\sqrt{3})$ is incident at an angle $30^{\circ}$ with the normal to the line $x=1$ at the point $A$. The ray gets reflected on the line $x=1$ and meets the $x$-axis at the point $B$. Then,the line $AB$ passes through the point

If $p = a_1 x + b_1 y + k_1 = 0$,$q = a_2 x + b_2 y + k_2 = 0$ and $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{k_1}{k_2}$,then the curve $p + c q = 0$ is

The equations of the lines which pass through the point of intersection of the lines $4x - 3y - 1 = 0$ and $2x - 5y + 3 = 0$ and are equally inclined to the axes are