The points $(2,3)$ and $\left(-4,-\frac{4}{3}\right)$ lie on the opposite sides of the line $L \equiv 5 x-6 y+k=0$ and k is an integer. If the points $(1,2)$ and $(4,5)$ lie on the same side of the line $L=0$, then the perpendicular distance from origin to the line $L=0$ is

If the incentre of the triangle formed by the lines $x-2=0, x+y-1=0, x-y+3=0$ is $(\alpha, \beta)$, then $\beta=$

If the equation of the pair of straight lines intersecting at ( $a, b$ ) and perpendicular to the pair of lines $3 x^2-4 x y+5 y^2=0$ is $l x^2+2 n x y+m y^2-32 x-26 y+c=0$, then $\frac{a+b+c}{l+h+m}=$

$P Q R$ is a right-angled isosceles triangle with right angle at $P(2,1)$. If the equation of the line $Q R$ is $2 x+y=3$, then the equation representing the pair of lines $P Q$ and $P R$ is