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

If $(a, 1/a)$,$(b, 1/b)$,$(c, 1/c)$,and $(d, 1/d)$ are four distinct points on a circle of radius $4$ units,then $abcd$ is equal to

If a circle passes through points $(4,0)$ and $(0,2)$ and its centre lies on the $Y$-axis. If the radius of the circle is $r$,then the value of $r^2-r+1$ is

The equation of a circle whose centre lies at the point $(-2, 1)$ and which passes through the point $(4, 3)$ is:

If the lines $2x + 3y + 1 = 0$ and $3x - y - 4 = 0$ are diameters of a circle with circumference $10\pi$,find the equation of the circle.

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