SOLUTION: If the circle is tangent to the line -3x+2y+1=0 at the point (1, 1), and the center is an the line x+y-1=0. Find the general equation of the circle.

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Question 1168435: If the circle is tangent to the line -3x+2y+1=0 at the point (1, 1), and the center is an the line x+y-1=0. Find the general equation of the circle.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
If the circle is tangent to the line -3x+2y+1=0 at the point (1, 1), and the
center is an the line x+y-1=0. Find the general equation of the circle.


Let the equation of the circle be:

%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2

Then the tangent point (1,1) is on the circle, so

%281-h%29%5E2%2B%281-k%29%5E2=r%5E2

The center (h,k) lies on the line 

x%2By-1=0, so

h%2Bk-1=0

The perpendicular distance from the center (h,k), to the tangent line, 
which is
-3x%2B2y%2B1=0

is the radius r (in green), so

%28-3h%2B2k%2B1%29%2Fsqrt%2813%29=%22%22+%2B-+r

So we have the system of three equations in three unknowns:



Can you find the solution?

The solution is (h,k,r) = (-2,3,√13)

So the equation of the circle is

(x+2)2 + (y-3)2 = 13 

If you have trouble finding the solution to the system,
tell me about it in the thank you message below, and I'll
get back to you by email.  No charge.

Edwin