The combined equation of the diagonals of the square formed by the pairs of lines $xy+6y-4x-24=0$ and $xy+6x-4y-24=0$ is

If the area of the triangle formed by the pair of lines $8x^2-6xy+y^2=0$ and the line $2x+3y=a$ is $7$,then $a$ is equal to

The area (in square units) of the triangle formed by the line $x+y+1=0$ and the pair of straight lines $x^2-3xy+2y^2=0$ is

If the slopes of both the lines given by $x^2 + 2hxy + 6y^2 = 0$ are positive and the angle between these lines is $\operatorname{Tan}^{-1}\left(\frac{1}{7}\right)$,then the product of the perpendiculars from the point $(1, 1)$ to these lines is:

If two pairs of straight lines with combined equations $xy+4x-3y-12=0$ and $xy-3x+4y-12=0$ form a square,then the combined equation of its diagonals is

The area bounded by the angle bisectors of the lines ${x^2} - {y^2} + 2y = 1$ and the line $x + y = 3$ is: