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

Let the equation $x^{2}+y^{2}+px+(1-p)y+5=0$ represent circles of varying radius $r \in (0, 5]$. Then the number of elements in the set $S = \{q : q = p^{2} \text{ and } q \text{ is an integer}\}$ is ..... .

The equation of the circle touching the lines $|x-2|+|y-3|=4$ is

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

If the radius of a circle is $a$ and it touches the $X$-axis at the origin,then its equation is....

Find the Cartesian equation of the circle whose parametric equations are $x = -7 + 4 \cos \theta$ and $y = 3 + 4 \sin \theta$.