SOLUTION: Find the equation that is satisfied by the coordinates of the centers of the set of circles that are tangent to the line whose equations are 5x+12y-39=0 and 12x-5y-13=0.

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Question 1128285: Find the equation that is satisfied by the coordinates of the centers of the set of circles that are tangent to the line whose equations are 5x+12y-39=0 and 12x-5y-13=0.
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
In slope-intercept form, the two lines are:
y = (-5/12)x + 3.25
y = (12/5)x - 2.6
The distances from the center of the circles to each of the tangent lines are the same
and are equal to the radius of the circles
The centers of the circles must therefore lie on an angle bisector between the two lines.
The slope and intercept of the "acute" bisector is given by:
ma = tan((atan(m1) + atan(m2))/2) where m1 and m2 are the slopes of the 2 lines
ba = m1(b2-b1)/(m2-m1) + b1 - ma(b2-b1)/(m2-m1)
The "obtuse" bisector is found in a similar way.
The equations for the two lines are:
y = 0.41165x + 1.52941
y = -2.42857x + 7.42857
The centers of the circles are represented by these two equations