Find the equation of the circle which passes through the origin and cuts off chords of lengths 4 and 6 on the positive side of the x-axis and y-axis respectively.

Explanation

To find the equation of the circle that passes through the origin and cuts off chords of lengths 4 and 6 on the positive sides of the x-axis and y-axis respectively, we can follow these steps:

### Step 1: Identify the points on the circle
Since the circle passes through the origin (0, 0), and it cuts off a chord of length 4 on the x-axis, we can determine that one endpoint of this chord is at (4, 0). Similarly, since it cuts off a chord of length 6 on the y-axis, one endpoint of this chord is at (0, 6). Thus, the points we have are:
- Point A: (0, 0) (the origin)
- Point B: (4, 0) (on the x-axis)
- Point C: (0, 6) (on the y-axis)

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