document.write( "Question 1142649: Find the equation of the circle tangent to $\"2x-3y%2B6+=+0\"$ at (-3,0) and \r
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Algebra.Com's Answer #763353 by ikleyn(52909) $\"\"$ $\"About$

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document.write( "The center of this circle lies on the straight line perpendicular to the given line and passing through the point (-3,0).\r\n" );
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document.write( "From the other side, the center of this circle lies on the perpendicular bisector to the segment connecting the points (-3,0) and (-3,6).\r\n" );
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document.write( "Notice that this segment, connecting the points (-3,0) and (-3,6), is VERTICAL and its middle point is (-3,3).\r\n" );
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document.write( "So, that perpendicular bisector is simply the horizontal line y = 3.\r\n" );
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document.write( "Perpendicular to the given line has an equation\r\n" );
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document.write( "    3x + 2y = c,      (1)\r\n" );
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document.write( "where \"c\" is unknown constant.\r\n" );
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document.write( "Since this perpendicular line (1) passes through the point (-3,0), we have\r\n" );
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document.write( "   3*(-3) + 2*0 = c = -9.\r\n" );
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document.write( "Thus, the center of the circle lies on the line\r\n" );
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document.write( "    3x + 2y = -9\r\n" );
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document.write( "and on the line  y =3  at the same time,  which gives you\r\n" );
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document.write( "    3x + 2*3 = -9,\r\n" );
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document.write( "    3x       = -9 - 6 = -15,\r\n" );
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document.write( "     x                = -15/3 = -5.\r\n" );
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document.write( "Thus the center of the circle is the point (x,y) = (-5,3).\r\n" );
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document.write( "Since the distance from the center of the circle to the point (-3,0) is\r\n" );
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document.write( "     =  = ,\r\n" );
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document.write( "the radius of the circle is .\r\n" );
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document.write( "Then the equation of the circle in the standard form is\r\n" );
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document.write( "     +  = ,\r\n" );
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document.write( "or, equivalently,\r\n" );
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document.write( "     +  = 13.      ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to see many other similar solved problems, you can find them in the lesson\r
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