Equation of a circle | Mathematico

In the picture below, the point $A$ is always a distance of $3$ away from the fixed point $C (1, 2)$ . Try moving $A$ around to see what happens.

The shape is a circle. If the coordinates of $A$ are $(x, y)$ , then, by the distance formula, we must have

\sqrt{(x - 1)^{2} + (y - 2)^{2}} = 3

More generally, if a circle has centre $(a, b)$ and radius $r$ , then $(x, y)$ lies on the circle if, and only if,

\sqrt{(x - a)^{2} + (y - b)^{2}} = r

It is customary to square both sides, giving the equation of a circle:

(x - a)^{2} + (y - b)^{2} = r^{2}

Write down the equation of a circle with radius $3 \sqrt{3}$ and centre $(6, - 3) .$ Sketch this circle, indicating all intersections with the coordinate axes.
A circle has equation
$x^{2} + y^{2} - 14 x + 8 y = 60$
Work out the coordinates of the centre of the circle and the radius of the circle.