The equation of a circle with center at $(-2, 3)$ and circumference of $4 \pi$ units is

If $\alpha$ and $\beta$ are the roots of $x^2+2x-3=0$ and $\gamma$ and $\delta$ are the roots of $y^2-y-6=0$,then the equation of the circle having $(\alpha, \gamma)$ and $(\beta, \delta)$ as ends of a diameter is

Four distinct points $(2k, 3k), (1, 0), (0, 1),$ and $(0, 0)$ lie on a circle for $k$ equal to:

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 smallest circle passing through the points $(2,2)$ and $(3,3)$ is

$A$ circle is drawn with the $y$-axis as a tangent and its center at the point which is the reflection of $(3, 4)$ in the line $y = x$. The equation of the circle is: