Question 1168234: Find the general equation of the circle, if the circle is tangent to the line -3x+2y+1=0 at the point (1, 1), and the center is on the line x+y-1=0.
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! Find the general equation of the circle,
if the circle is tangent to the line  at the point ( , ), then radius on the line  is perpendicular to tangent line
so,
hence, 
perpendicular line containing radius, will have a slope:
 ......plug in m and the point (, )
the center ( ,  ) is the point of intersection of perpendicular line and 
.........eq.1
.............eq.2
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substitute in eq.1
intersection point is ( ,  )
so, (, ) =(, )
 , 
Length of radius = distance from line to center (, ) and it is
the equation of the circle
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