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:

If the equations of the opposite sides of a parallelogram are $x^2 - 7x + 6 = 0$ and $y^2 - 14y + 40 = 0$,then the equation of one of its diagonals is

If $\frac{x^2}{a} + \frac{y^2}{b} + \frac{2xy}{h} = 0$ represents a pair of straight lines and the slope of one line is twice the other,then $ab : h^2$ is

If $(a, b)$ is the centroid of the triangle formed by the lines $4x^2 - 17xy + 4y^2 = 0$ and $x + y - 5 = 0$,and $c$ is the numerical value of the area of the triangle,then $a + b + c =$

If $2x^2 - 3xy + y^2 = 0$ represents two sides of a triangle and $x + y - 1 = 0$ is its third side,then the distance between the orthocenter and the circumcentre of that triangle is