Circle

If the circles \({x^2} + {y^2} + 6x + 8y + 16 = 0\) and \({x^2} + {y^2} + 2\left( {3 - \sqrt 3 } \right)x + 2\left( {4 - \sqrt 6 } \right)y = k + 6\sqrt 3 + 8\sqrt 6\), \(k > 0\), touch internally at the point \(P(\alpha ,\beta )\), then \({\left( {\alpha + \sqrt 3 } \right)^2} + {\left( {\beta + \sqrt 6 } \right)^2}\) is equal to ________________.