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 3cm from the end in contact with the x-axis.

Explanation

To solve the problem step by step, we will determine the equation of the locus of point P on the rod that is 3 cm from the end in contact with the x-axis.

### Step 1: Understand the Setup
We have a rod of length 12 cm that moves with its ends always touching the coordinate axes. Let’s denote the ends of the rod as points A and B, where A is on the x-axis and B is on the y-axis. The coordinates of point A can be represented as (x, 0) and the coordinates of point B as (0, y).

### Step 2: Relate the Length of the Rod to the Axes
Since the length of the rod is constant at 12 cm, we can use the distance formula to relate the coordinates of points A and B:
\[
...