Find the equation of a circle:
1)Which touches both the axes at a distance of 6 units from the origin.
2)Which touches x-axis at a distance 5 from the origin and radius 6 units
3)Which touches both the axes and passes through the point (2,1)
4)Passing through the origin, radius 17 and ordinate of the centre is -15.

Explanation

To find the equations of the circles for each part of the question, we will follow a systematic approach.

### Part 1: Circle touching both axes at a distance of 6 units from the origin.

1. **Identify the center**: Since the circle touches both the x-axis and y-axis at a distance of 6 units from the origin, the center of the circle can be at (6, 6), (-6, 6), (-6, -6), or (6, -6).

2. **Determine the radius**: The radius of the circle is equal to the distance from the center to either axis, which is 6 units.

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