The pairs of straight lines $x^2-3xy+2y^2=0$ and $x^2-3xy+2y^2+x-2=0$ form a

The area of the triangle formed by the lines $y^2 - 9xy + 18x^2 = 0$ and $y = 9$ 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

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

The combined equation of the diagonals of the square formed by the pairs of lines $xy+6y-4x-24=0$ and $xy+6x-4y-24=0$ is

The orthocentre of the triangle formed by the lines $x+3y=10$ and $6x^2+xy-y^2=0$ is