Find an equation of the circle and sketch it if the center is on line x–y = 6 and circle is tangent to both axes

(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