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Answer:
(x - 3)² + (y + 3)² = 9
Step-by-step explanation:
x–y = 6 y = x - 6
y intercept x = 0 y = -6 (0 , -6)
x intercept y = 0 x = 6 (6 , 0)
if circle center is on line x - y = 6 and tangent to both x and Y axis
the distance from center to X axis and Y axis should be equal, it's the mid-point of segment of x intercept and y intercept
center (h , k) h = (0 + 6) / 2 = 3 k = (0 + (-6)) / 2 = -3
center (3 , -3) radius = 3
Equation of circle: (x - h)² + (y - k)² = r² (x - 3)² + (y + 3)² = 9
