The joint equation of the straight lines $x + y = 1$ and $x - y = 4$ is

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

The lines ${a^2}{x^2} + bc{y^2} = a(b + c)xy$ will be coincident,if

If $\frac{x^2}{a} + \frac{2xy}{h} + \frac{y^2}{b} = 0$ represents a pair of straight lines such that the slope of one of the lines is twice the other,then $\frac{ab}{h^2} =$

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 slope of one of the lines represented by $ax^2+2hxy+by^2=0$ is the square of the other,then $\frac{a+b}{h}+\frac{8h^2}{ab}$ is equal to: