The equation of the perpendiculars drawn from the origin to the lines represented by the equation $2x^2 - 10xy + 12y^2 + 5x - 16y - 3 = 0$ is

The joint equation of two lines passing through the origin,each of which makes an angle of $30^{\circ}$ with the line $x+y=0$,is

The joint equation of a pair of straight lines passing through the origin and having slopes $(1+\sqrt{2})$ and $\left(\frac{1}{1+\sqrt{2}}\right)$ is $......$

If the sum of the slopes of the pair of lines represented by $4x^2 + 2hxy - 7y^2 = 0$ is equal to the product of the slopes,then the value of $h$ is

The equation of a pair of lines is given by a second-degree homogeneous equation. If one of them is perpendicular to the line $x+2y+7=0$ and the other is parallel to the line $3x+4y+5=0$,then the equation of that pair of lines is:

The equation $xy + a^2 = a(x + y)$ represents