If $\theta$ is the acute angle between the pair of lines $H \equiv a x^2-x y+b y^2=0, \tan \theta=5$ and $(1,-1)$ is a point on $H=0$, then $a^2+a b+b^2=$

The equation of the pair of straight lines passing through the point $(2,3)$ and perpendicular to the pair of lines $3 x^2-4 x y+5 y^2=0$ is $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$, then $a+b+c+f+g+h=$

If $f(x, y)=0$ is the combined equation of the lines joining the origin to the points where the line $4 x-6 y-2=0$ meets the curve $3 x^2-4 x y+5 y^2-2 x+y-6=0$, then $\frac{f(1,-1)}{f(-1,-1)}=$

If the line $2 x-y-4=0$ divides the line segment joining the points $(2,-1)$ and $(1,-4)$ at the point $(a, b)$ in the ratio $m: n$, then $4\left(a-b\left(\frac{m}{n}\right)^2\right)=$