Solve the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 - x } { y - 3 }$$
giving the particular solution that satisfies the condition \(y = 4\) when \(x = 5\).
Show that this particular solution can be expressed in the form
$$( x - a ) ^ { 2 } + ( y - b ) ^ { 2 } = k$$
where the values of the constants \(a , b\) and \(k\) are to be stated.
Hence sketch the graph of the particular solution, indicating clearly its main features.