The equation of one of the lines represented by the equation $pq(x^2 - y^2) + (p^2 - q^2)xy = 0$ is

If the slopes of the lines given by the equation $ax^{2} + 2hxy + by^{2} = 0$ are in the ratio $5:3$,then the ratio $h^{2}:ab$ is:

The equation $4x^2 - 24xy + 11y^2 = 0$ represents

The joint equation of two lines passing through $(-2, 3)$ and parallel to the bisectors of the angle between the co-ordinate axes 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

The value of $k$ for which the equation $x^2-4xy-y^2+6x+2y+k=0$ represents a pair of straight lines is equal to ........