Answer:
(x – 3)² + (y + 3)² = 3²
Step-by-step explanation:
The equation of a circle is:
(x − h)² + (y − k)² = r²
where (h, k) is the center and r is the radius.
If the circle is tangent to both axes, then |h| = |k| = r.
If the center is on the line x – y = 6, then h – k = 6.
If h and k have the same sign:
h = k
h = h – 6
0 = -6
So h and k must have different signs:
h = -k
h = -(h – 6)
h = -h + 6
2h = 6
h = 3
Therefore, the center is (3, -3) and the radius is 3. Meaning the equation of the circle is:
(x – 3)² + (y + 3)² = 3²
Here's a graph: desmos.com/calculator/4gqmifzsmm
