$A$ second degree homogeneous equation in $x$ and $y$ always represents:

The equation $x^2 - 7xy + 12y^2 = 0$ represents

If the slopes of the lines given by the equation $ax^{2} + 2hxy + by^{2} = 0$ are in the ratio $5:3$,then the ratio $h^{2}:ab$ is:

If the slopes of the lines represented by the equation $6x^2 + 2hxy + 4y^2 = 0$ are in the ratio $2:3$,then the value of $h$ such that both the lines make acute angles with the positive $X$-axis measured in the positive direction is

If one of the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ bisects the angle between the coordinate axes in the first quadrant,then which of the following is true?

The combined equation of the lines passing through the point $(3,4)$ and each making an angle $45^{\circ}$ with the line $x+y+1=0$ is