If the circles $S \equiv x^2+y^2-14x+6y+33=0$ and $S' \equiv x^2+y^2-a^2=0$ where $a \in \mathbb{N}$ have $4$ common tangents,then the possible number of values of $a$ is:

The sum of the squares of the lengths of the chords intercepted on the circle,$x^2 + y^2 = 16$,by the lines,$x + y = n$,$n \in N$,where $N$ is the set of all natural numbers,is

If $(\frac{1}{10}, \frac{-1}{5})$ is the inverse point of a point $(-1, 2)$ with respect to the circle $x^2 + y^2 - 2x + 4y + c = 0$,then $c =$

The two circles $x^2 + y^2 - 2x + 6y + 6 = 0$ and $x^2 + y^2 - 5x + 6y + 15 = 0$:

The ratio of the largest and shortest distances from the point $(2, -7)$ to the circle $x^2 + y^2 - 14x - 10y - 151 = 0$ is

Observe the following statements:
$I$. The circle $x^2+y^2-6x-4y-7=0$ touches the $y$-axis.
$II$. The circle $x^2+y^2+6x+4y-7=0$ touches the $x$-axis.
Which of the following is a correct statement?