The area enclosed by the curve $x = \sqrt{3} \cos \theta, y = \sqrt{3} \sin \theta$ is

If two vertices of an equilateral triangle are $A(-a, 0)$ and $B(a, 0)$,where $a > 0$,and the third vertex $C$ lies above the $x$-axis,then the equation of the circumcircle of $\Delta ABC$ is:

Let a circle passing through $(2,0)$ have its centre at the point $(h, k)$. Let $(x_c, y_c)$ be the point of intersection of the lines $3x + 5y = 1$ and $(2+c)x + 5c^2y = 1$. If $h = \lim_{c \to 1} x_c$ and $k = \lim_{c \to 1} y_c$,then the equation of the circle is:

The radius of the circle $r = \sqrt{3} \sin \theta + \cos \theta$ is

The radius of the larger circle lying in the first quadrant and touching the line $4x + 3y - 12 = 0$ and the coordinate axes is:

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