A rod AB of length 15 cm rests in between two coordinate axes in such a way that the end point A lies on x-axis and end point B lies on y-axis. A point P(x, y) is taken on the rod in such a way that AP = 6 cm. Show that the locus of P is an ellipse.

Explanation

To solve the problem step by step, we will follow the reasoning provided in the video transcript and derive the equation of the locus of point P.

### Step 1: Understand the configuration
We have a rod AB of length 15 cm, where point A lies on the x-axis and point B lies on the y-axis. Let the coordinates of point A be (x_A, 0) and point B be (0, y_B). Since the length of the rod is 15 cm, we can express this relationship as:
\[ x_A + y_B = 15 \]

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