document.write( "Question 1019836: Find the equation of the circle touching the line 4x-3y=28 at (4,-4) and passing through (-3,-5).
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Algebra.Com's Answer #635768 by Alan3354(69443)![]() ![]() You can put this solution on YOUR website! Find the equation of the circle touching the line 4x-3y=28 at (4,-4) and passing through (-3,-5). \n" ); document.write( "--------------------------- \n" ); document.write( "The center of the circle is on the line perpendicular to the given line thru (4,-4). \n" ); document.write( "The slope of the line is -3/4 --> y+4 = (-3/4)*(x-4) \n" ); document.write( "--> y = -3x/4 - 1 \n" ); document.write( "---- \n" ); document.write( "The slope of a line tangent to a circle is -x/y. \n" ); document.write( "The center of the circle is also on the line perpendicular to the tangent line thru (-3,-5). \n" ); document.write( "The slope of the tangent line = -3/5. \n" ); document.write( "The slope of the line perpendicular = 5/3 \n" ); document.write( "--> y+5 = (5/3)*(x+3) \n" ); document.write( "--> y = 5x/3 \n" ); document.write( "----------------------------- \n" ); document.write( "The center of the circle is the intersection of y = 5x/3 and y = -3x/4 - 1 \n" ); document.write( "5x/3 = -3x/4 - 1 \n" ); document.write( "20x = -9x - 12 \n" ); document.write( "x = -12/29 --> y = -20/29 \n" ); document.write( "Center at (-12/29,-20/29) \n" ); document.write( "---- \n" ); document.write( "r = distance from the center to (4,-4) \n" ); document.write( " \n" ); document.write( "------------------ \n" ); document.write( " \n" ); document.write( "==================================================== \n" ); document.write( "Something is wrong, I'll check it later. \n" ); document.write( "------ \n" ); document.write( "I can't find the error. If you can't find it, repost it, maybe someone else will do it. \n" ); document.write( "================== \n" ); document.write( "I see what the problem is. A slope of -x/y for a circle applies to circles centered at the Origin. \n" ); document.write( "I'll work on this later today. \n" ); document.write( " |