The range of a random variable $$X$$ is $$\{1,2,3, \ldots\}$$ and $$P(X=x)=\frac{C^x}{x !}$$. for $$x=1,2,3$$, ... Then, the value of $$C$$ is

Tom and Jerry play a game of alternately throwing an unfair coin. First one to get head wins. If Tom starts the game, he has 62.5% chance of winning the game. Suppose this coin is tossed 5 times, then the probability of getting exactly 3 head is

A point moves so that the sum of its distances from $$(a e, 0)$$ and $$(-a e, 0)$$ is $$2 a$$, then the equation to its locus, where $$b^2=a^2\left(1-e^2\right)$$ is

The point to which the origin should be shifted in order to eliminate the $$x$$ and $$y$$ terms from the equation $$9 x^2+4 y^2+10 x+12 y+1=0$$ is