Find the equation of the circle with center at $(0,0)$ and radius $r$.

Find the equation of the circle with radius $5$ whose centre lies on the $x-$axis and passes through the point $(2, 3)$.

$A$ circle is drawn with the $y$-axis as a tangent and its center at the point which is the reflection of $(3, 4)$ in the line $y = x$. The equation of the circle is:

$A$ circle passing through the points $(1, 1)$ and $(2, 0)$ touches the line $3x - y - 1 = 0$. If the equation of this circle is $x^2 + y^2 + 2gx + 2fy + c = 0$,then a possible value of $g$ is

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

The number of integral values of $\lambda$ for which $x^2 + y^2 + \lambda x + (1 - \lambda)y + 5 = 0$ is the equation of a circle whose radius cannot exceed $5$ is: