The area of the triangle formed by the lines $y^2 - 9xy + 18x^2 = 0$ and $y = 9$ is

If the sides of a triangle $ABC$ are $2x^2-y^2=0$ and $x+y-1=0$,and the sides of another triangle $PQR$ are $2x^2-5xy+2y^2=0$ and $7x-2y-12=0$,then the distance between the centroid of $\triangle ABC$ and the orthocentre of $\triangle PQR$ 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

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:

One line of the pair of lines $x^2+xy-2y^2=0$ is perpendicular to one line of the pair of lines $3y^2-5xy-2x^2=0$. If the combined equation of the two lines other than those two perpendicular lines is $ax^2+2hxy+by^2=0$,then $a+2h+b=$

The difference of the tangents of the angles which the lines $(\tan ^2 \alpha+\cos ^2 \alpha) x^2-2 x y \tan \alpha +(\sin ^2 \alpha) y^2=0$ make with the $X$-axis is