$A(-2, 3)$ is a point on the line $4x + 3y - 1 = 0$. If the points on the line that are $10$ units away from the point $A$ are $(x_1, y_1)$ and $(x_2, y_2)$,then $(x_1 + y_1)^2 + (x_2 + y_2)^2 =$

If $(1, 5)$ is the midpoint of the segment of a line between the lines $5x - y - 4 = 0$ and $3x + 4y - 4 = 0$, then the equation of the line is:

Let the area of the triangle formed by a straight line $L : x + by + c = 0$ with the coordinate axes be $48$ square units. If the perpendicular drawn from the origin to the line $L$ makes an angle of $45^{\circ}$ with the positive $x$-axis,then the value of $b^2 + c^2$ is:

Three lines $x + 2y + 3 = 0$,$x + 2y - 7 = 0$,and $2x - y - 4 = 0$ form three sides of two squares. Find the equation of the fourth side of each square.

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

Consider the fourteen lines in the plane given by $y=x+r$ and $y=-x+r$,where $r \in \{0, 1, 2, 3, 4, 5, 6\}$. The number of squares formed by these lines,whose sides are of length $\sqrt{2}$,is: