The value of $p$ for which the equation $x^2+pxy+y^2-5x-7y+6=0$ represents a pair of straight lines is:

The equation of the pair of lines perpendicular to the lines represented by $x^2-5xy+4y^2=0$ and passing through the point $(2,1)$ is

The pair of straight lines that passes through the point $(1, 2)$ and is perpendicular to the pair of straight lines $3x^2 - 8xy + 5y^2 = 0$ is:

The equation of the pair of straight lines,each of which makes an angle $\alpha$ with the line $y = x$,is

If one of the lines of the pair $ax^{2}+2hxy+by^{2}=0$ bisects the angle between the positive direction of the axes,then $a, b,$ and $h$ satisfy the relation:

The combined equation of a possible pair of adjacent sides of a square with area $16 \text{ square units}$ whose centre is the point of intersection of the lines $x+2y-3=0$ and $2x-y-1=0$ is