If ${g^2} + {f^2} = c$,then the equation ${x^2} + {y^2} + 2gx + 2fy + c = 0$ will represent

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

The equation of the circle concentric with the circle $x^2+y^2-6x+12y+15=0$ and having double its area 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:

$A$ line meets the coordinate axes at points $A$ and $B$. $A$ circle is circumscribed about the triangle $OAB$. If $m$ and $n$ are the distances of the tangents to the circle at points $A$ and $B$ respectively from the origin,then the diameter of the circle is

$A$ circle touches both axes and its center lies in the fourth quadrant. If its radius is $1$,then its equation is: