Sunday 15 August 2021

Consider the curves \(x^{2}+y^{2}-4 x-6 y-12=0,\space 9 x^{2}+4 y^{2}-900=0\) and \(y^{2}-6 y-6 x+51=0.\) The maximum number of disjoint regions into which these curves divide the \(XY\)-plane (excluding the curves themselves), is
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