(9 cos \(\alpha\), 9 sin \(\alpha\))
Let P (h, k) be any point on the required path
From the given information, we have
h = 9 cos \(\alpha\) and k = 9 sin \(\alpha\)
\(\Rightarrow\)  \({{h}\over{9}}\) = cos \(\alpha\) and \({{k}\over{9}}\) = sin \(\alpha\)
\({\left({{h}\over{9}} \right)}^{2}+{\left({{k}\over{9}} \right)}^{2}=cos^2\alpha+sin^2\alpha\)
\(\Rightarrow\)  \({{h^2}\over{81}}+{{k^2}\over{81}}=1\)     \([\because sin^2\ \alpha+cos^2\ \alpha=1]\)
\(\Rightarrow\)  h²+ k² = 81
\(\therefore\)  Locus of (h, k) is x² + y² = 81