The number of straight lines that can be drawn through the point $(2, 5)$ which form a triangle of area $24 \text{ sq. units}$ with the coordinate axes is:

The lines $x + y = |a|$ and $ax - y = 1$ intersect each other in the first quadrant. Then,in which interval do all possible values of $a$ lie?

The point on the line $4x - y - 2 = 0$ which is equidistant from the points $(-5, 6)$ and $(3, 2)$ is:

If a line $ax + 2y = k$ forms a triangle of area $3$ sq. units with the coordinate axes and is perpendicular to the line $2x - 3y + 7 = 0$,then the product of all the possible values of $k$ is

If a straight line is passing through the point of intersection of the lines $3x - 4y + 1 = 0$ and $5x + y - 1 = 0$ and making equal non-zero intercepts on the coordinate axes,then the area (in sq. units) of the triangle formed by this line with the coordinate axes is

The least distance from the origin to a point on the line $y=x+3$ which lies at a distance of $2$ units from $(0,3)$ is