document.write( "Question 1087452: Write the equation of the circle havhng radius 13square root and tangent to the line 2x - 3y + 1 = 0 at (1,1) \n" ); document.write( "
Algebra.Com's Answer #701758 by Fombitz(32388)\"\" \"About 
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Find the line perpendicular to the tangent line through (1,1).
\n" ); document.write( "\"2x-3y%2B1=0\"
\n" ); document.write( "\"3y=2x%2B1\"
\n" ); document.write( "\"y=%282%2F3%29x%2B1%2F3\"
\n" ); document.write( "Perpendicular lines have slopes that are negative reciprocals,
\n" ); document.write( "\"%282%2F3%29m%5Bp%5D=-1\"
\n" ); document.write( "\"m%5Bp%5D=-3%2F2\"
\n" ); document.write( "\"y-1=-%283%2F2%29%28x-1%29\"
\n" ); document.write( "Find the center of the circle (x,y) using the radius from (1,1),
\n" ); document.write( "\"%28x-1%29%5E2%2B%28y-1%29%5E2=13\"
\n" ); document.write( "From above,
\n" ); document.write( "\"%28y-1%29%5E2=%28-%283%2F2%29%28x-1%29%29%5E2\"
\n" ); document.write( "\"%28y-1%29%5E2=%289%2F4%29%28x-1%29%5E2\"
\n" ); document.write( "Substituting,
\n" ); document.write( "\"%28x-1%29%5E2%2B%28y-1%29%5E2=13\"
\n" ); document.write( "\"%28x-1%29%5E2%2B%289%2F4%29%28x-1%29%5E2=13\"
\n" ); document.write( "\"%2813%2F4%29%28x-1%29%5E2=13\"
\n" ); document.write( "\"%28x-1%29%5E2=4\"
\n" ); document.write( "\"x-1=0+%2B-+2\"
\n" ); document.write( "\"x=-1\" and \"x=3\"
\n" ); document.write( "Solving for y,
\n" ); document.write( "\"x=-1\"
\n" ); document.write( "\"y-1=-%283%2F2%29%28-1-1%29\"
\n" ); document.write( "\"y=4\"
\n" ); document.write( "Solving for y,
\n" ); document.write( "\"x=3\"
\n" ); document.write( "\"y-1=-%283%2F2%29%283-1%29\"
\n" ); document.write( "\"y=-2\"
\n" ); document.write( "So then the two circles are,
\n" ); document.write( "\"+%28x%2B1%29%5E2%2B%28y-4%29%5E2=13+\"
\n" ); document.write( "\"+%28x-3%29%5E2%2B%28y%2B2%29%5E2=13+\"
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