SOLUTION: Find an equation of the circle: Center on line x - y = 6, tangent to both axes I changed the equation to y=x-6 and then I don't know how to solve/do the next step.

Algebra ->  Circles -> SOLUTION: Find an equation of the circle: Center on line x - y = 6, tangent to both axes I changed the equation to y=x-6 and then I don't know how to solve/do the next step.      Log On


   

Question 1134372: Find an equation of the circle:
Center on line x - y = 6, tangent to both axes
I changed the equation to y=x-6 and then I don't know how to solve/do the next step.
Answer by greenestamps(13334) About Me  (Show Source):
You can put this solution on YOUR website!


If the circle is tangent to both axes, then the center of the circle is the same distance from both axes. Mathematically, that means

abs%28y%29=abs%28x%29

which is equivalent to

y=x or y=-x

So you are looking for the solution of the system

y+=+x-6 AND (y=x OR y=-x)

If you don't immediately see where the center of the circle is, here is a graph; y=x-6 (red); y = x (green); and y = -x (blue):

graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx-6%2Cx%2C-x%29

The center of the circle is at the only point where the red line intersects either the green or blue line.

Then it should be clear what the radius of the circle is; and I will assume you know how to write the equation once you know the center of the circle and the radius.