The figure formed by the pairs of lines $6x^2+13xy+6y^2=0$ and $6x^2+13xy+6y^2+10x+10y+4=0$ is a

The area (in square units) of the triangle formed by the lines $6 x^2+13 x y+6 y^2=0$ and $x+2 y+3=0$ is

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

The coordinates of the orthocentre of the triangle formed by the lines $2x^2 - 2y^2 + 3xy + 3x + y + 1 = 0$ and $3x + 2y + 1 = 0$ are:

Area of the triangle bounded by the lines given by the equations $12 x^2-20 x y+7 y^2=0$ and $x+y-1=0$ is

Let $OABC$ be a parallelogram. The equation of one diagonal $AC$ is $x+y-1=0$ and the combined equation of the sides $OA, OC$ is $2x^2-y^2=0$. If $G$ is the centroid of the triangle $OAC$,then $BG=$