document.write( "Question 319800: Find the coordinates of the center of the circle and length of the radius given the equation of that circle which is $\"5x%5E2%2B15x%2B5y%5E2-10y-10=0\"$ \n" ); document.write( "

Algebra.Com's Answer #229049 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"5x%5E2%2B15x%2B5y%5E2-10y-10=0\"$
\n" ); document.write( "

\r\n" );
document.write( "We need to get it in the form  so we'll\r\n" );
document.write( "know it has center (h,k) and radius r.\r\n" );
document.write( "\r\n" );
document.write( "First we add 10 to both sides to get the constant off the left side:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next we divide through by the common coefficient of x² and y² which\r\n" );
document.write( "is 5\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Put the addition of one blank after the 3x and another after the -2y since we\r\n" );
document.write( "are going to add something to both sides\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next we calculate what goes in the first blank:\r\n" );
document.write( "\r\n" );
document.write( "1. Multiply the coefficient of x, which is 3, by }, getting \r\n" );
document.write( "2. Square that value:  , so  is what goes\r\n" );
document.write( "in the first blank, and we also add it to the right side:\r\n" );
document.write( "\r\n" );
document.write( "  \r\n" );
document.write( "\r\n" );
document.write( "Next we calculate what goes in the second blank:\r\n" );
document.write( "\r\n" );
document.write( "1. Multiply the coefficient of y, which is -2, by }, getting \r\n" );
document.write( "2. Square that value:  , so  is what goes\r\n" );
document.write( "in the second blank, and we also add it to the right side:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The first three terms on the left  factors as  or \r\n" );
document.write( "\r\n" );
document.write( "The last three terms on the left  factors as  or \r\n" );
document.write( "\r\n" );
document.write( "The right side  becones \r\n" );
document.write( "\r\n" );
document.write( "So we now have:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And we compare that to \r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "and we see that since , , and\r\n" );
document.write( "since , . Also  so }\r\n" );
document.write( "\r\n" );
document.write( "Edwin

.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );