Find the equation of a circle with radius $4$ that touches the $x$-axis at a distance of $-3$ from the origin.

The radius of a circle which touches the $y$-axis at $(0,3)$ and cuts an intercept of $8$ units with the $x$-axis is

The equation of the circle with radius $5$ and touching the coordinate axes in the third quadrant is:

The abscissae of two points $A$ and $B$ are the roots of the equation $x^2+2ax-b^2=0$ and their ordinates are roots of the equation $y^2+2py-q^2=0$. Then the equation of the circle with $AB$ as diameter is given by

$A$ 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

$P$ and $Q$ are the points of trisection of the line segment joining the points $(3, -7)$ and $(-5, 3)$. If $PQ$ subtends a right angle at a variable point $R$,then the locus of $R$ is