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

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10.416 meters per second

step-by-step explanation:

distance=1 00 meters

time= 9.6 seconds in decimal form or 9 3/5 as a mixed number

average speed= 100/9.6

=10.416 meters per second or 10 52/125 as a mixed number.