One of the lines represented by the equation ${x^2} + 6xy = 0$ is

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

The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0$. Then the value of $k$ is:

If the equation $\lambda x^{2} + 2y^{2} - 5xy + 5x - 7y + 3 = 0$ represents a pair of straight lines,then $\lambda = \dots$

If the slope of one line of the pair of lines $2x^2 + hxy + 6y^2 = 0$ is thrice the slope of the other line,then $h =$

If $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$ represents a pair of lines,which of the following statements is true?