SOLUTION: how to solve this find the equation of the circle describe here.. {{the circle is tangent to the line 2x-y=3 at the point (2,1) and the center is on the x-axis}} tnx.

Algebra ->  Circles -> SOLUTION: how to solve this find the equation of the circle describe here.. {{the circle is tangent to the line 2x-y=3 at the point (2,1) and the center is on the x-axis}} tnx.      Log On


   

Question 206197: how to solve this
find the equation of the circle describe here..
{{the circle is tangent to the line 2x-y=3 at the point (2,1) and the center is on the x-axis}}
tnx.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
at the point of tangency, the radius of the circle is perpendicular to the tangent line

perpendicular lines have slopes that are negative reciprocals

so the slope of a radius is -1/2 ___ it passes through (2,1) ___ and the other end is on the x-axis (y = 0)

the center of the circle is (4,0) ___ this is down 1 and over 2 from (2,1)

by Pythagoras, the radius squared is 2^2 + 1^2 ___ so r^2 = 5

the equation of the circle is ___ (x - 4)^2 + (y - 0)^2 = 5