The equation $(x + y)^2 - (x^2 + y^2) = 0$ represents

If $L{x^2} - 10xy + 12{y^2} + 5x - 16y - 3 = 0$ represents a pair of straight lines,then the value of $L$ is:

If one of the lines in the pair of straight lines given by $4x^2+6xy+ky^2=0$ bisects the angle between the coordinate axes,then $k \in$

The equation of the pair of straight lines perpendicular to the pair $2 x^2+3 x y+2 y^2+10 x+5 y=0$ and passing through the origin is $..........$

If $ax^2-34xy-5y^2+2x+26y-5=0$ represents a pair of straight lines,then the value of $a$ is

$A$ pair of straight lines drawn through the origin forms an isosceles triangle right-angled at the origin with the line $2x + 3y = 6$. The area (in sq. units) of the triangle so formed is