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

Find the centre and the radius of the circle $x^{2}+y^{2}+8x+10y-8=0$.

$A$ circle has its equation in the form $x^2 + y^2 + 2x + 4y + 1 = 0$. Choose the correct coordinates of its centre and the right value of its radius from the following:

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

The circle passing through the point $(-1, 0)$ and touching the $y$-axis at $(0, 2)$ also passes through the point

The equation of the circumcircle of the triangle formed by the lines $x = 0$,$y = 0$,and $2x + 3y = 5$ is