If the lines represented by the equation $px^2 - qy^2 = 0$ are distinct,then:

If the distance of two lines passing through the origin from the point $({x_1}, {y_1})$ is $d$,then the equation of the lines is:

The equation $2x^2 + 4xy - py^2 + 4x + qy + 1 = 0$ will represent two mutually perpendicular straight lines,if

The equation of the pair of straight lines passing through the point $(1,1)$ and perpendicular to the pair of straight lines $3x^2-8xy+5y^2=0$ is

If the sum of the slopes of the lines represented by the equation $x^2 - 2xy \tan A - y^2 = 0$ is $4$,then $\angle A = $

If the equation of the pair of straight lines passing through the point $(1, 1)$ and perpendicular to the pair of lines $3x^2 + 11xy - 4y^2 = 0$ is $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ (where the constant term is $12$),then find the value of $2(a - h + b - g + f - 12)$.