SOLUTION: 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.

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
-----------------------

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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