Question 678416: Find the equation of the circle if it is tangent to the line x+y=2 at point (4,-2) and the center at x-axis.
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website!
(h,k)-center and r radius
given:
given:
the circle if it is tangent to the line  at point ( , ) and the center at 
find the equation of the circle:
Let ... C( , ) be the center.
Also, let the line L : touch
this circle at the point A(,)
Line   has slope 
and slope of seg AC is  .
Since line L is perpendicular to segment AC, 
Hence, C ≡ (,) ≡ ( ,)
and
 .
Hence, by Center-Radius Form, eq of circle is:
 ......... your answer
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