If the locus of a point which is equidistant from the coordinate axes forms a triangle with the line $y=3$,then the area of the triangle is

If the algebraic sum of the distances from the points $(2,0)$,$(0,2)$,and $(1,1)$ to a variable straight line is zero,then the line passes through the fixed point:

$A$ variable line passes through a fixed point $P$. If the algebraic sum of the perpendiculars drawn from $(2, 0)$,$(0, 2)$,and $(1, 1)$ to the line is zero,then the coordinates of the point $P$ are:

The locus of $P$ such that the area of $\Delta PAB = 12 \text{ sq. units}$,where $A(2, 3)$ and $B(-4, 5)$ is:

If the sum of the distances of a point $P(x, y)$ from two perpendicular lines in a plane is $1$,then the locus of $P$ is a

If the point $\left(\alpha, \frac{7 \sqrt{3}}{3}\right)$ lies on the curve traced by the mid-points of the line segments of the lines $x \cos \theta + y \sin \theta = 7, \theta \in \left(0, \frac{\pi}{2}\right)$ between the coordinate axes,then $\alpha$ is equal to