document.write( "Question 718034: Please help Transform to standard form and describe the graph of each equation.
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Algebra.Com's Answer #440707 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Those are all equations of circles and they are all done the same way,\r\n" );
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document.write( "I'll do the 2nd one as it is the most complete and the 3rd one is weird:\r\n" );
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document.write( "2. 36x²+36y²+36y=48x+199\r\n" );
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document.write( "Get the x-term next to the x² term and the y-term next to the y² term.\r\n" );
document.write( "Get only the constant term on the right.\r\n" );
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document.write( "36x²-48x + 36y² + 36y = 199 \r\n" );
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document.write( "Divide every term through by the common coefficient of the x²\r\n" );
document.write( "and the y² terms, which is 36\r\n" );
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document.write( "x² - \"48%2F36\"x + y² + y = \"199%2F36\"\r\n" );
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document.write( "Reduce the fraction \"48%2F36\" to \"4%2F3\"\r\n" );
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document.write( "x² - \"4%2F3\"x + y² + y = \"199%2F36\"\r\n" );
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document.write( "Complete the squares on the lft:\r\n" );
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document.write( "1. Multiply the coefficient of x, which is \"-4%2F3\", by \"1%2F2\",\r\n" );
document.write( "getting \"-2%2F3\".\r\n" );
document.write( "2. Square this result, getting \"%28-2%2F3%29%5E2\" = \"4%2F9\"\r\n" );
document.write( "3. Add this right after the x term on the left side and also \r\n" );
document.write( "add it to the right side.\r\n" );
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document.write( "1. Multiply the coefficient of y, which is 1, by \"1%2F2\",\r\n" );
document.write( "getting \"1%2F2\".\r\n" );
document.write( "2. Square this result, getting \"%281%2F2%29%5E2\" = \"1%2F4\"\r\n" );
document.write( "3. Add this right after the y term on the left side and also \r\n" );
document.write( "add it to the right side.\r\n" );
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document.write( "x² - \"4%2F3\"x + \"4%2F9\" + y² + y + \"1%2F4\" = \"199%2F36\" + \"4%2F9\" + \"1%2F4\"\r\n" );
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document.write( "Factor the first three terms as (x - \"2%2F3\")(x - \"2%2F3\") which can be\r\n" );
document.write( "written as the square (x - \"2%2F3\")².\r\n" );
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document.write( "Factor the last three terms on the left as (y - \"1%2F2\")(y - \"1%2F2\") which can be \r\n" );
document.write( "written as the square (y - \"1%2F2\")².\r\n" );
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document.write( "Combine the terms on the right by getting an LCD of 36\r\n" );
document.write( "\"199%2F36\" + \"4%2F9\" + \"1%2F4\" = \"199%2F36\" + \"16%2F36\" + \"9%2F36\" = \"%28199%2B16%2B9%29%2F36\" = \"224%2F36\" = \"56%2F9\"\r\n" );
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document.write( "(x - \"2%2F3\")² + (y - \"1%2F2\")² = \"56%2F9\"\r\n" );
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document.write( "That is a circle with center (\"2%2F3\",\"1%2F2\") and radius \"expr%284%2F3%29sqrt%2814%29\".\r\n" );
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document.write( "9x²+9y²+6x=-5\r\n" );
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document.write( "Get the x-term next to the x² term and the y-term next to the y² term.\r\n" );
document.write( "The constant term is already on the right.\r\n" );
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document.write( "9x² + 6x + 9y² = -5\r\n" );
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document.write( "Divide every term through by the common coefficient of the x²\r\n" );
document.write( "and the y² terms, which is 9:\r\n" );
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document.write( "x² - \"6%2F9\"x + y² = \"-5%2F9\"\r\n" );
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document.write( "Reduce the fraction \"6%2F9\" to \"2%2F3\"\r\n" );
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document.write( "x² - \"2%2F3\"x + y² = \"-5%2F9\"\r\n" );
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document.write( "Complete the squares on the left:\r\n" );
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document.write( "1. Multiply the coefficient of x, which is \"-2%2F3\", by \"1%2F2\",\r\n" );
document.write( "getting \"-1%2F3\".\r\n" );
document.write( "2. Square this result, getting \"%28-1%2F3%29%5E2\" = \"1%2F9\"\r\n" );
document.write( "3. Add this right after the x term on the left side and also \r\n" );
document.write( "add it to the right side.\r\n" );
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document.write( "Since there is no y term, write y² as (y - 0)²\r\n" );
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document.write( "x² - \"4%2F3\"x + \"1%2F9\" + (y - 0)² = \"-5%2F9\" + \"1%2F9\"\r\n" );
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document.write( "Factor the first three terms as (x - \"1%2F3\")(x - \"1%2F3\") which can be\r\n" );
document.write( "written as the square (x - \"1%2F3\")².\r\n" );
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document.write( "Combine the terms on the right:\r\n" );
document.write( "\"-5%2F9\" + \"1%2F9\" = \"-4%2F9\"\r\n" );
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document.write( "(x - \"1%2F9\")² + (y - 0)² = \"-4%2F9\"\r\n" );
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document.write( "That is an imaginary circle with a real center of (\"1%2F9\",0) and an imaginary\r\n" );
document.write( "radius of \"2%2F3\"i.  Really weird.  Was that -5 on the right supposed to be 5?\r\n" );
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document.write( "Edwin
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