If the equation of a line having a slope $m$ $(m \in \mathbb{Z})$,passing through $(1, 1)$ and making an angle of $\tan^{-1}\left(\frac{5}{7}\right)$ with the line $x + y - 3 = 0$ is $ax + y + c = 0$,then $ac =$

$A$ straight line through the origin bisects the line segment joining the points $(a \cos \alpha, a \sin \alpha)$ and $(a \cos \beta, a \sin \beta)$. Then the lines are

What are the equations of the two lines passing through the point $(7, 9)$ and making an angle of $60^{\circ}$ with the line $x - \sqrt{3}y - 2\sqrt{3} = 0$?

$A$ 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

If $A (-2, 1)$,$B (2, 3)$,and $C (-2, -4)$ are three points,then what is the angle between $BA$ and $BC$?

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