document.write( "Question 153717: What is the graph of the equation x2 + y2 - 8x + 6y + 24 = 0 \n" ); document.write( "

Algebra.Com's Answer #113148 by Edwin McCravy(20054) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "This is a circle because $\"x%5E2\"$ and $\"y%5E2\"$ have the
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2+%2B+y%5E2+-+8x+%2B+6y+%2B+24+=+0\"$
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document.write( "We must first get the equation in standard form:\r\n" );
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document.write( "Rearrange to get the x terms together and the y terms togethsr.\r\n" );
document.write( "That is, swap the middle two terms:\r\n" );
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document.write( "Out to the side or on scratch paper,\r\n" );
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document.write( "we complete the square of\r\n" );
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document.write( "1. Multiply the coefficient, -8, of , by ,\r\n" );
document.write( "   getting .\r\n" );
document.write( "2. Then square , getting +16\r\n" );
document.write( "3. Add +16 to the left side inside the first parentheses, and\r\n" );
document.write( "   also add it to the right side:\r\n" );
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document.write( "   \r\n" );
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document.write( "Now we complete the square of\r\n" );
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document.write( "1. Multiply the coefficient, 6, of , by ,\r\n" );
document.write( "   getting .\r\n" );
document.write( "2. Then square , getting +9\r\n" );
document.write( "3. Add +9 to the left side inside the first parentheses, and\r\n" );
document.write( "   also add it to the right side:\r\n" );
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document.write( "Factor each parentheses:\r\n" );
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document.write( "Write as perfect squares:\r\n" );
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document.write( "Add -24 to both sides:\r\n" );
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document.write( "Compare to the standard form:\r\n" );
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document.write( "This has center (h,k) and radius r.\r\n" );
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document.write( " so , , so .  , so \r\n" );
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document.write( "so the center, (h,k) = (4,-3) and the radius is 1.\r\n" );
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document.write( "So we plot the center (4,-3).\r\n" );
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document.write( "Get a compass and open it one unit wide.  Place the sharp \r\n" );
document.write( "point of the compass on the center and draw the circle.\r\n" );
document.write( "That is the graph:\r\n" );
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document.write( "Edwin

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