If the product of the lengths of the perpendiculars drawn from the point $(-1, 5)$ to the pair of lines $2x^2 - xy + ky^2 + 6x + y + 4 = 0$ is $\frac{65}{\sqrt{26}}$,then $37k^2 + 92k$ is equal to

The area (in square units) of the quadrilateral formed by the two pairs of lines $l^2x^2 - m^2y^2 - n(lx + my) = 0$ and $l^2x^2 - m^2y^2 + n(lx - my) = 0$ is

If the lines represented by $2x^2 + 6xy + y^2 = 0$ are $L_1$ and $L_2$,and the lines represented by $4x^2 + 18xy + y^2 = 0$ are $l_1$ and $l_2$,and the acute angle between $L_1$ and $l_1$ is $\theta$,then the acute angle between $L_2$ and $l_2$ is :-

The equation of a line which makes an angle of $45^{\circ}$ with each of the pair of lines $xy-x-y+1=0$ is

The combined equation of the diagonals of the square formed by the two pairs of straight lines given by $xy+4x-3y-12=0$ and $xy-3x+4y-12=0$ 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 $\frac{a+b+c}{l+h+m} =$