(c) x2 + y2 ± 10x ± 10y + 25 = 0
Case I: If the circle lies in the first quadrant:
The equation of a circle that touches both the coordinate axes and has radius a is .
The given radius of the circle is 5 units, i.e. .
Thus, the equation of the circle is .
Case II: If the circle lies in the second quadrant:
The equation of a circle that touches both the coordinate axes and has radius a is .
The given radius of the circle is 5 units, i.e. .
Thus, the equation of the circle is .
Case III: If the circle lies in the third quadrant:
The equation of a circle that touches both the coordinate axes and has radius a is .
The given radius of the circle is 5 units, i.e. .
Thus, the equation of the circle is .
Case IV: If the circle lies in the fourth quadrant:
The equation of a circle that touches both the coordinate axes and has radius a is .
The given radius of the circle is 5 units, i.e. .
Thus, the equation of the circle is .
Hence, the required equation of the circle is x2 + y2 ± 10x ± 10y + 25 = 0.