SOLUTION: There are two circles that go through (9,2). Each one is tangent to both coordinateaxes. Find the center and the radius for each circle. Start by drawing a clear diagram.

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: There are two circles that go through (9,2). Each one is tangent to both coordinateaxes. Find the center and the radius for each circle. Start by drawing a clear diagram.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1163741: There are two circles that go through (9,2). Each one is tangent to both coordinateaxes. Find the center and the radius for each circle. Start by drawing a clear diagram.
Answer by greenestamps(13334) About Me  (Show Source):
You can put this solution on YOUR website!


The centers of both circles are equidistant from both axes; so let the coordinates of the centers of the circles be (h,h).

Using the distance formula to say that the distance from (9,2) to (h,h) is equal to h should give us two values for h, giving us the centers of the two circles.

%28h-9%29%5E2%2B%28h-2%29%5E2+=+h%5E2
h%5E2-18h%2B81%2Bh%5E2-4h%2B4+=+h%5E2

That is indeed a quadratic equation; it will give us two solutions.

I leave it to you to do the work to finish the problem.

Note both values of h are whole numbers; if you're not getting that result, something is wrong with your work....