The two lines represented by the equation $x^2 + xy + y^2 = 0$ are

If $s$ and $p$ are respectively the sum and the product of the slopes of the lines $3x^2 - 2xy - 15y^2 = 0$,then $s:p$ is equal to

If the distance of two lines passing through the origin from the point $({x_1}, {y_1})$ is $d$,then the equation of the lines 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

If the slopes of the lines represented by $ax^{2} + 2hxy + by^{2} = 0$ are in the ratio $1 : 3$,then $h^{2} : ab =$

The equations of the lines represented by the equation $ab(x^2 - y^2) + (a^2 - b^2)xy = 0$ are