The points of contact of the circle $x^2 + y^2 + 2x + 2y + 1 = 0$ with the coordinate axes are:

The Cartesian equation of the curve given by $x = 6 \cos \theta$ and $y = 6 \sin \theta$ is

The equation of the circle passing through the points $(1, 0)$ and $(0, 1)$ with the smallest radius is . . . . . .

If the endpoints of a diameter of a circle are $(1, 2)$ and $(3, 4)$,then its equation is:

Consider a family of circles which are passing through the point $(-1, 1)$ and are tangent to the $x$-axis. If $(h, k)$ are the coordinates of the center of the circles,then the set of values of $k$ is given by the interval:

$A$ circle has its centre in the first quadrant and passes through $(2,3)$. If this circle makes intercepts of length $3$ and $4$ respectively on $x=2$ and $y=3$,its equation is