A random variable $X$ follows a binomial distribution in which the difference between its mean and variance is 1. if $2 P(x=2)=3 P(x=1)$, then $n^2 P(x>1)=$

If the distance of a variable point $P$ from a point $A(2,-2)$ is twice the distance of $P$ from $Y$-axis, then the equation of locus of $P$ is

If the transformed equation of the equation $2 x^2+3 x y-2 y^2-17 x+6 y+8=0$ after translating the coordinate axes to a new origin ( $\alpha, \beta$ ) is $a X^2+2 h X Y+b Y^2+c=0$, then $3 \alpha+c=$

$P(6,4)$ is a point on the line $x-y-2=0$. If $A(\alpha, \beta)$ and $B(\gamma, \delta)$ are two points on this line lying on either side of $P$ at a distance of 4 units from $P$, then $\alpha^2+\beta^2+\gamma^2+\delta^2=$