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

The area (in sq units) of the quadrilateral formed by two pairs of lines $\lambda^2 x^2 - m^2 y^2 - n(\lambda x + my) = 0$ and $\lambda^2 x^2 - m^2 y^2 + n(\lambda x + my) = 0$ is:

Suppose the pairs of straight lines $2x^2 + axy + 3y^2 = 0$ and $2x^2 + bxy - 3y^2 = 0$ are such that they have one common line,and the other two lines are perpendicular. Then the values of $a$ and $b$ are respectively:

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

If the pair of straight lines given by $Ax^2+2Hxy+By^2=0$ $(H^2>AB)$ forms an equilateral triangle with the line $ax+by+c=0$,then $(A+3B)(3A+B)$ is equal to:

If the centroid of the triangle formed by the lines $2y^2+5xy-3x^2=0$ and $x+y=k$ is $(\frac{1}{18}, \frac{11}{18})$,then the value of $k$ equals $..........$