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

If the bisectors of the angles of the lines represented by $3x^2 - 4xy + 5y^2 = 0$ and $5x^2 + 4xy + 3y^2 = 0$ are the same,then the angle made by the lines represented by the first equation with the second is .....$^o$.

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

If one of the lines given by the equation $2x^2 + axy + 3y^2 = 0$ coincides with one of those given by the equation $2x^2 + bxy - 3y^2 = 0$,while the other two lines are perpendicular to each other,then the values of $a$ and $b$ are

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