The line $x+y=1$ meets the lines represented by the equation $y^3-6xy^2+11x^2y-6x^3=0$ at the points $P, Q, R$. If $O$ is the origin,then $(OP)^2+(OQ)^2+(OR)^2=$

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 :-

If the pair of lines represented by $3x^2 - 5xy + Py^2 = 0$ and $6x^2 - xy - 5y^2 = 0$ have one line in common,then the sum of all possible values of $P$ is

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

The triangle formed by the lines $2x^2+xy-6y^2=0$ and $x+y-1=0$ is

The orthocentre of the triangle formed by the lines $x+y=1$ and $2y^2-xy-6x^2=0$ is