Minimum Distance in a 3-Dimensional Space

Geometry Level pending

Let \(D\) be the minimum distance between \(x = 2y^{2}+3z^{2}\) and \(x+8y+18z+36 = 0\). What is the value of \(\frac{1}{D^{2}}\)?

\(\textit{Proposed by Tommy} \)

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