If one of the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ is $y = mx$,then

If the equation $ax^{2} + by^{2} + cx + cy = 0$,$c \neq 0$ represents a pair of lines,then

The joint equation of a pair of lines passing through the point $(1, 4)$, where one line is parallel to the $X$-axis and the other makes an angle of $45^\circ$ with the positive direction of the $X$-axis, is:

If $ad \neq 0$ and two of the lines represented by $ax^3+3bx^2y+3cxy^2+dy^3=0$ are perpendicular,then

If $p_1$ and $p_2$ denote the lengths of perpendiculars from $(2,3)$ onto the lines given by $15 x^2+31 x y+14 y^2=0$,and if $p_1 > p_2$,then $p_1^2 + \frac{1}{74} - p_2^2 + \frac{1}{13}$ is equal to

If the equation $x^2 + y^2 + 2gx + 2fy + 1 = 0$ represents a pair of straight lines,then: