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

The equation of a circle which touches the $x$-axis and whose centre is $(1, 2)$ is

Find the area of the circle given by the equation $(x+1)(x+2)+(y-1)(y+3)=0$.

Let in an equilateral $\Delta ABC,$ $A(-1 + a \cos \theta, 2 + a \sin \theta),$ $B(-1 + a \cos \alpha, 2 - a \sin \alpha),$ and $C(-1 + a \sin \beta, 2 + a \cos \beta).$ If the length of the median through vertex $A$ is $2b,$ then the equation of the circumcircle of triangle $ABC$ is (where $a$ is a constant) -

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

$A$ circle passes through the points $(2,0)$ and $(1,2)$. If the power of the point $(0,2)$ with respect to this circle is $4$,then the radius of the circle is