8 A curve has equation \(y = k x ^ { \frac { 3 } { 2 } }\) where \(k\) is a constant.
The point \(P\) on the curve has \(x\)-coordinate 4.
The normal to the curve at \(P\) is parallel to the line \(2 x + 3 y = 0\) and meets the \(x\)-axis at the point \(Q\). The line \(P Q\) is the radius of a circle centre \(P\). Show that \(k = \frac { 1 } { 2 }\).
Find the equation of the circle.