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

If the lines represented by $2x^2 + 6xy + y^2 = 0$ are $L_1$ and $L_2$,and the lines represented by $4x^2 + 18xy + y^2 = 0$ are $l_1$ and $l_2$,and the acute angle between $L_1$ and $l_1$ is $\theta$,then the acute angle between $L_2$ and $l_2$ 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 $BG=$

The equation of a line which makes an angle of $45^{\circ}$ with each of the pair of lines $xy-x-y+1=0$ is

If two sides of a triangle are given by $3x^2-5xy+2y^2=0$ and its orthocentre is $(2,1)$,then the equation of the third side of the triangle is

If the angle between the pair of lines $x^2+2 \sqrt{2} x y+k y^2=0, k>0$ is $45^{\circ}$,then the area (in square units) of the triangle formed by the pair of bisectors of angles between the given lines and the line $x+2 y+1=0$ is