If $9x^2-24xy+16y^2+\alpha x+\beta y+6=0$ represents a pair of parallel lines $1$ unit apart and one of those lines passes through $(1,1)$,then $\frac{\alpha}{\beta} = $

If the pair of straight lines given by $Ax^2+2Hxy+By^2=0$ $(H^2>AB)$ forms an equilateral triangle with the line $ax+by+c=0$,then $(A+3B)(3A+B)$ is equal to:

If the lines represented by $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$ intersect on the $x$-axis,which of the following is in general incorrect?

If the sides of a triangle $ABC$ are $2x^2-y^2=0$ and $x+y-1=0$,and the sides of another triangle $PQR$ are $2x^2-5xy+2y^2=0$ and $7x-2y-12=0$,then the distance between the centroid of $\triangle ABC$ and the orthocentre of $\triangle PQR$ is

If the area of the triangle formed by the pair of lines $8x^2-6xy+y^2=0$ and the line $2x+3y=a$ is $7$,then $a$ is equal to

The pair of straight lines $x^2 - 4xy + y^2 = 0$ together with the line $x + y + 4 = 0$ form a triangle which is: