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

If the endpoints of a diameter of a circle are $(0, 1)$ and $(1, 1)$,then its equation is . . . .

The equation of the circle of radius $3$ that lies in the fourth quadrant and touches the lines $x=0$ and $y=0$ is

$(1, k)$ is a point on the circle passing through the points $(-1, 1), (0, -1)$ and $(1, 0)$. If $k \neq 0$,then $k =$

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 $C=$

The equation of the circle with radius $5$ and touching the coordinate axes in the third quadrant is: