Two straight lines $3x + 4y = 5$ and $4x - 3y = 15$ intersect at the point $A$. The equations of the lines passing through $(1, 2)$ and intersecting the given lines at $B$ and $C$ such that $AB = AC$ are

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

If the line segment joining the points $(5, 2)$ and $(2, a)$ subtends an angle $\frac{\pi}{4}$ at the origin,then the absolute value of the product of all possible values of $a$ is:

The acute angle between two straight lines passing through the point $M(-6, -8)$ and the points in which the line segment $2x + y + 10 = 0$ enclosed between the coordinate axes is divided in the ratio $1 : 2 : 2$ in the direction from the point of its intersection with the $x$-axis to the point of intersection with the $y$-axis is:

Find the angle between the lines joining the points $(0, 0), (2, 3)$ and $(2, -2), (3, 5)$.

Find the equation of the line passing through the point $(4, 5)$ and making equal angles with the lines $3x = 4y + 7$ and $5y = 12x + 6$.