The power of the point $(-3, 7)$ with respect to a circle,with centre $(3, 7)$ and radius $2$,is

If the equation $\frac{K(x + 1)^2}{3} + \frac{(y + 2)^2}{4} = 1$ represents a circle,then $K = $

The four distinct points $(0,0), (2,0), (0,-2)$ and $(k,-2)$ are concyclic,if $k$ is equal to

The lengths of the intercepts made by a circle $S$ on $X$ and $Y$-axes are $\frac{2 \sqrt{13}}{3}$ and $\frac{2 \sqrt{22}}{3}$ respectively. If the radius of the circle $S$ is $\frac{\sqrt{38}}{3}$ and its centre $C$ lies in the second quadrant,then $C=$

For what value of $k$,the points $(0, 0), (1, 3), (2, 4)$ and $(k, 3)$ are concyclic?

The equation of the circle with radius $\sqrt{17}$ units, whose centre lies on the positive side of the $x$-axis and which passes through the point $(0, 1)$, is: