If the equation $3x^{2}+10xy+3y^{2}+16y+k=0$ represents a pair of lines,then the value of $k$ is

If $4ab = 3h^2$,then the ratio of the slopes of the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ will be

The combined equation of the lines passing through the origin making an acute angle $\alpha$ with the line $y=x$ is

The joint equation of a pair of lines passing through the origin and making an angle of $\frac{\pi}{4}$ with the line $3x + 2y - 8 = 0$ is

If the pair of lines $3x^2 - 5xy + py^2 = 0$ and $6x^2 - xy - 5y^2 = 0$ have one line in common,then $p =$

If the lines represented by the equation $4xy + 6x - 8y + c = 0$ form a rectangle with the coordinate axes,then the area of the rectangle (in sq. units) is