The nature of the straight lines represented by the equation $4x^2 + 12xy + 9y^2 = 0$ is

If the sum of the slopes of the lines given by ${x^2} - 2cxy - 7{y^2} = 0$ is four times their product,then $c$ has the value

The equation of the pair of perpendicular lines passing through the origin and forming an isosceles right-angled triangle with the line $2x + 3y = 6$ is

The area of the triangle formed by the lines $3x^2 - 4xy + y^2 = 0$ and $2x - y = 6$ is:

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