If the combined equation of the diagonals of the square formed by the pairs of lines $xy+4x-5y-20=0$ and $xy-5x+4y-20=0$ is $x^2-y^2-kx+ly=0$,then $k+l=$.

The difference of the tangents of the angles which the lines $(\tan ^2 \alpha+\cos ^2 \alpha) x^2-2 x y \tan \alpha +(\sin ^2 \alpha) y^2=0$ make with the $X$-axis 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 the equation of the pair of straight lines intersecting at $(a, b)$ and perpendicular to the pair of lines $3x^2 - 4xy + 5y^2 = 0$ is $lx^2 + 2hxy + my^2 - 32x - 26y + c = 0$,then $\frac{a+b+c}{l+h+m} =$

The area of the triangle formed by the lines $y^2 - 9xy + 18x^2 = 0$ and $y = 9$ is ............ $sq. \, units$.

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