A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.

Question

$\begin {array} {1 1} (A)\;x^2+y^2=729 & \quad (B)\;x^2=9y \\ (C)\;\large\frac{x^2}{81}+\large\frac{y^2}{9}=1 & \quad (D)\;\large\frac{x^2}{81}-\large\frac{y^2}{9}=1 \end {array}$