document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #744891 by htmentor(1343) $\"\"$ $\"About$

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In slope-intercept form, the two lines are:
\n" ); document.write( "y = (-5/12)x + 3.25
\n" ); document.write( "y = (12/5)x - 2.6
\n" ); document.write( "The distances from the center of the circles to each of the tangent lines are the same
\n" ); document.write( "and are equal to the radius of the circles
\n" ); document.write( "The centers of the circles must therefore lie on an angle bisector between the two lines.
\n" ); document.write( "The slope and intercept of the \"acute\" bisector is given by:
\n" ); document.write( "ma = tan((atan(m1) + atan(m2))/2) where m1 and m2 are the slopes of the 2 lines
\n" ); document.write( "ba = m1(b2-b1)/(m2-m1) + b1 - ma(b2-b1)/(m2-m1)
\n" ); document.write( "The \"obtuse\" bisector is found in a similar way.
\n" ); document.write( "The equations for the two lines are:
\n" ); document.write( "y = 0.41165x + 1.52941
\n" ); document.write( "y = -2.42857x + 7.42857
\n" ); document.write( "The centers of the circles are represented by these two equations \n" ); document.write( "

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