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 $4\left(a-b\left(\frac{m}{n}\right)^2\right)=$
The distance between the points of concurrency of the two families of straight lines given by $x+(5 \lambda+1) y+1-3 \lambda=0$ and $(5 \mu+2) x-3 y+3+6 \mu=0$ is
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