JEE Quadratic #4

Geometry Level 4

\[y^{2}\big(y^{2}-6\big)+x^{2}-8x +24 =0\]

Given the above equation, if the minimum and maximum values of \(x^{2}+y^{4}\) are \(m\) and \(M\), respectively, then find the value of \(M-2m\).