If the probability distribution of a random variable $X$ is as follow, then the variance of $X$ is

$X=x$	2	3	5	9
$P(X=x)$	$k$	$2 k$	$3 k^2$	$k$

The mean of a binomial variate $X \sim B(n, p)$ is 1 . If $n>2$ and $P(X=2)=\frac{27}{128}$, then the variance of the distribution is

If the distance from a variable point $P$ to the point $(4,3)$ is equal to the perpendicular distance from $P$ to the line $x+2 y-1=0$, then the equation of the locus of the point $P$ is

$(0, k)$ is the point to which the origin is to be shifted by the translation of the axes so as to remove the first degree terms from the equation $a x^2-2 x y+b y^2-2 x+4 y+1=0$ and $\frac{1}{2} \tan ^{-1}(2)$ is the angle through which the coordinate axes are to be rotated about the origin to remove the $x y$-term from the given equation, then $a+b=$