The sides $AB, BC, CD$ and $DA$ of a quadrilateral are $x + 2y = 3, x = 1, x - 3y = 4$ and $5x + y + 12 = 0$ respectively. The angle between diagonals $AC$ and $BD$ is ......$^o$

The vertices of a triangle are $(at_1t_2, a(t_1 + t_2))$,$(at_2t_3, a(t_2 + t_3))$,and $(at_3t_1, a(t_3 + t_1))$. Find the coordinates of its orthocentre.

The circumradius of the triangle formed by the lines $xy+2x+2y+4=0$ and $x+y+2=0$ is

If a straight line $L$ is perpendicular to the line $4x - 2y = 1$ and forms a triangle of area $4 \text{ sq unit}$ with the coordinate axes,then the equation of the line $L$ is

If the lines $3x + y - 4 = 0$,$x - \alpha y + 10 = 0$,$\beta x + 2y + 4 = 0$,and $3x + y + k = 0$ represent the sides of a square,then $\alpha \beta (k + 4)^2 = $

$A$ square with each side of length $a$ lies above the $x$-axis and has one vertex at the origin. One of the sides passing through the origin makes an angle $\alpha$ $(0 < \alpha < \frac{\pi}{4})$ with the positive direction of the $x$-axis. Find the equations of the diagonals of the square.