document.write( "Question 253258: Need to turn this into standard form...
\n" ); document.write( "4x^2+4y^2-24+16y-100=0
\n" ); document.write( "4x^2+4y^2+16y=124
\n" ); document.write( "4x^2+4y^2+16Y+(1/2 of 16 =8^2=64)=124
\n" ); document.write( "4x^2 +4y^2+16y+64-64=124-64
\n" ); document.write( "4x^2 + 4y^2+16y=64
\n" ); document.write( "4x^2+ (2y+4)^2=64 or 8^2
\n" ); document.write( "I know this is not right but i do not know what to do.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #185548 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\"4x%5E2%2B4y%5E2-24%2B16y-100=0\"\r
\n" ); document.write( "\n" ); document.write( "\"4x%5E2%2B4y%5E2-24%2B16y-100=0\"\r
\n" ); document.write( "\n" ); document.write( "\"4x%5E2%2B4y%5E2%2B16y-124=0\"
\n" ); document.write( "
\r\n" );
document.write( "First of all notice that every term is divisible by 4,\r\n" );
document.write( "so let's divide every term by 4:\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2%2By%5E2%2B4y-31=0\"\r\n" );
document.write( "\r\n" );
document.write( "Let's add 31 to both sides:\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2%2By%5E2%2B4y=31\"\r\n" );
document.write( "\r\n" );
document.write( "Let's complete the square of the last two terms \"y%5E2%2B4x\"\r\n" );
document.write( "on the left side.  We take the coefficient of y, which is 4, \r\n" );
document.write( "multiply it by \"1%2F2\", getting 2, then we square 2, and \r\n" );
document.write( "\"2%5E2\" is 4, so we add \"%22%22%2B4\" to both sides:\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2%2By%5E2%2B4y\"\"red%28%22%2B4%22%29=31\"\"red%28%22%2B4%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "Let's put parentheses around the last three terms on the left\r\n" );
document.write( "side and combine the terms on the right:\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2%2B%28y%5E2%2B4y%2B4%29=35\"\r\n" );
document.write( "\r\n" );
document.write( "Now factor the trinomials in the parentheses:\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2%2B%28y%2B2%29%28y%2B2%29=35\"\r\n" );
document.write( "\r\n" );
document.write( "That can be written as\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2%2B%28y%2B2%29%5E2=35\"\r\n" );
document.write( "\r\n" );
document.write( "In fact you could have skipped the step before that.\r\n" );
document.write( "\r\n" );
document.write( "The standard form for a circle is\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "Since you didn't have to complete the square on the\r\n" );
document.write( "x term, because you only had an \"x%5E2\" term and\r\n" );
document.write( "no x-term, then to get it in the standard form you\r\n" );
document.write( "have to write \"x%5E2\" as \"%28x-0%29%5E2\" to have the\r\n" );
document.write( "standard form, so the answer is\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-0%29%5E2%2B%28y%2B2%29%5E2=35\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "is the equation of a circle\r\n" );
document.write( "\r\n" );
document.write( "which has center (h,k) and radius r\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-0%29%5E2%2B%28y%2B2%29%5E2=35\"\r\n" );
document.write( "\r\n" );
document.write( "is the equation for a circle which has center\r\n" );
document.write( "\r\n" );
document.write( "(0,-2) and radius \"sqrt%2835%29\" which is about 5.92\r\n" );
document.write( "\r\n" );
document.write( "and has this graph:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "----------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Are you sure there wasn't supposed to be an x after the -24?\r\n" );
document.write( "The reason I ask that is I don't think when you are advanced \r\n" );
document.write( "enough to be studying circles, that your teacher would \r\n" );
document.write( "still be testing you on such an elementary thing as to see \r\n" );
document.write( "whether you could combine the terms -24 and -100.  So I'm going \r\n" );
document.write( "to assume you really meant:\r\n" );
document.write( "\r\n" );
document.write( "\"4x%5E2%2B4y%5E2-24red%28x%29%2B16y-100=0\"\r\n" );
document.write( "\r\n" );
document.write( "First of all notice that every term is divisible by 4,\r\n" );
document.write( "so let's divide every term by 4:\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2%2By%5E2-6x%2B4y-25=0\"\r\n" );
document.write( "\r\n" );
document.write( "Let's group the the two terms in x first and the two terms\r\n" );
document.write( "in y second, and add 25 to both sides:\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2-6x%2By%5E2%2B4y=25\"\r\n" );
document.write( "\r\n" );
document.write( "To complete the square of the first two terms \"x%5E2-6x\"\r\n" );
document.write( "we take the coefficient of x, which is -6, multiply it by \"1%2F2\",\r\n" );
document.write( "getting -3, then we square -3, and \"%28-3%29%5E2\" is 9, so we add \"%22%22%2B9\"\r\n" );
document.write( "to both sides:\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2-6x\"\"red%28%22%2B9%22%29%2By%5E2%2B4y=25\"\"red%28%22%2B9%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "Let's put parentheses around the first three terms and\r\n" );
document.write( "combinethe terms on the right.\r\n" );
document.write( "\r\n" );
document.write( "\"%28x%5E2-6x%2B9%29%2By%5E2%2B4y=34\"\r\n" );
document.write( "\r\n" );
document.write( "Now lwt's complete the square of the last two terms \"y%5E2%2B4x\"\r\n" );
document.write( "on the left side.  We take the coefficient of y, which is 4, \r\n" );
document.write( "multiply it by \"1%2F2\", getting 2, then we square 2, and \r\n" );
document.write( "\"2%5E2\" is 4, so we add \"%22%22%2B4\" to both sides:\r\n" );
document.write( "\r\n" );
document.write( "\"%28x%5E2-6x%2B9%29%2By%5E2%2B4y\"\"red%28%22%2B4%22%29=34\"\"red%28%22%2B4%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "Let's put parentheses around the last three terms on the left\r\n" );
document.write( "side and combine the terms on the right:\r\n" );
document.write( "\r\n" );
document.write( "\"%28x%5E2-6x%2B9%29%2B%28y%5E2%2B4y%2B4%29=38\"\r\n" );
document.write( "\r\n" );
document.write( "Now factor the trinomials in the two parentheses:\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-3%29%28x-3%29%2B%28y%2B2%29%28y%2B2%29=38\"\r\n" );
document.write( "\r\n" );
document.write( "That can be written as\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-3%29%5E2%2B%28y%2B2%29%5E2=38\"\r\n" );
document.write( "\r\n" );
document.write( "In fact you could have skipped the step before that.\r\n" );
document.write( "\r\n" );
document.write( "That's the standard form for a circle \r\n" );
document.write( "\r\n" );
document.write( "\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "which has center (h,k) and radius r\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-3%29%5E2%2B%28y%2B2%29%5E2=38\"\r\n" );
document.write( "\r\n" );
document.write( "is the equation for a circle which has center\r\n" );
document.write( "\r\n" );
document.write( "(3,-2) and radius \"sqrt%2838%29\" which is about 6.16\r\n" );
document.write( "\r\n" );
document.write( "and has this graph:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );