document.write( "Question 266969: This is a three part question. I wasn't too sure where to post it, so I posted the question here.\r
\n" ); document.write( "\n" ); document.write( "Given the equation of the circle, label the center and radius of the circle.
\n" ); document.write( "A) X^2 + 2x + y^2 + 10y - 23 = 0\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "B) X^2 + 4X + y^2 - 12y = 24\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "C) X^2 + 10X + y^2 - 11 = 0
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #196044 by Edwin McCravy(20056) $\"\"$ $\"About$
You can put this solution on YOUR website!
\r\n" );
document.write( "You must get these in the standard form\r\n" );
document.write( "for a circle\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the center is (h,k) and the radius is r.\r\n" );
document.write( "\r\n" );
document.write( "A)  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Get the constant term on the right by\r\n" );
document.write( "adding  to both sides:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply the coefficient of ,\r\n" );
document.write( "which is  by , getting\r\n" );
document.write( ". Then square ,\r\n" );
document.write( "getting  and add to\r\n" );
document.write( "both sides, putting it right after the\r\n" );
document.write( " on the left:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factor the first three terms on the left,\r\n" );
document.write( "and combine the numbers on the right\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And write  as \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply the coefficient of ,\r\n" );
document.write( "which is  by , getting\r\n" );
document.write( ".  Then square ,\r\n" );
document.write( "getting  and add to\r\n" );
document.write( "both sides, putting it right after the\r\n" );
document.write( " on the left:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factor the last three terms on the left,\r\n" );
document.write( "and combine the numbers on the right\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And write  as \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and write  as \r\n" );
document.write( "\r\n" );
document.write( ", which we compare to\r\n" );
document.write( "\r\n" );
document.write( ", and so\r\n" );
document.write( "\r\n" );
document.write( "since  then , and\r\n" );
document.write( "\r\n" );
document.write( "since  then , and \r\n" );
document.write( "\r\n" );
document.write( "so the center is (h,k) = (-1,-5) and the radius is r=7.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "B)  \r\n" );
document.write( "\r\n" );
document.write( "Exactly the same way:\r\n" );
document.write( "\r\n" );
document.write( "The constant term is already on the right,\r\n" );
document.write( "so we don't have to get it over there.\r\n" );
document.write( "\r\n" );
document.write( "Multiply the coefficient of ,\r\n" );
document.write( "which is  by , getting\r\n" );
document.write( ". Then square ,\r\n" );
document.write( "getting  and add to\r\n" );
document.write( "both sides, putting it right after the\r\n" );
document.write( " on the left:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factor the first three terms on the left,\r\n" );
document.write( "and combine the numbers on the right\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And write  as \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply the coefficient of ,\r\n" );
document.write( "which is  by , getting\r\n" );
document.write( ".  Then square ,\r\n" );
document.write( "getting  and add to\r\n" );
document.write( "both sides, putting it right after the\r\n" );
document.write( " on the left:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factor the last three terms on the left,\r\n" );
document.write( "and combine the numbers on the right\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And write  as \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and write  as \r\n" );
document.write( "\r\n" );
document.write( ", which we compare to\r\n" );
document.write( "\r\n" );
document.write( ", and so\r\n" );
document.write( "\r\n" );
document.write( "since  then , and\r\n" );
document.write( "\r\n" );
document.write( "since  then , and \r\n" );
document.write( "\r\n" );
document.write( "so the center is (h,k) = (-2,6) and the radius is r=8.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "C) \r\n" );
document.write( "\r\n" );
document.write( "This is just like the other except it'e a little\r\n" );
document.write( "easier because we don't have to complete the square \r\n" );
document.write( "of y because there is no term in y, so we do something \r\n" );
document.write( "else there. But we begin the same way:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Get the constant term on the right by\r\n" );
document.write( "adding  to both sides:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply the coefficient of ,\r\n" );
document.write( "which is  by , getting\r\n" );
document.write( ". Then square ,\r\n" );
document.write( "getting  and add to\r\n" );
document.write( "both sides, putting it right after the\r\n" );
document.write( " on the left:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factor the first three terms on the left,\r\n" );
document.write( "and combine the numbers on the right\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And write  as \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now the only thing we have to do is write the\r\n" );
document.write( "term  as \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Then write the 36 on the right as \r\n" );
document.write( "\r\n" );
document.write( ", which we compare to\r\n" );
document.write( "\r\n" );
document.write( ", and so\r\n" );
document.write( "\r\n" );
document.write( "since  then , and\r\n" );
document.write( "\r\n" );
document.write( "since  then , and \r\n" );
document.write( "\r\n" );
document.write( "so the center is (h,k) = (5,0) and the radius is r=6.\r\n" );
document.write( "\r\n" );
document.write( "Now be sure to learn how to do this by practicing on\r\n" );
document.write( "\r\n" );
document.write( "some other problems like these, because even though I\r\n" );
document.write( "\r\n" );
document.write( "can do your homework for you, I can't pass your tests\r\n" );
document.write( "\r\n" );
document.write( "that you take in class for you, and your homework won't \r\n" );
document.write( "\r\n" );
document.write( "do you any good if you flunk the tests, because your \r\n" );
document.write( "\r\n" );
document.write( "teacher will then know you just got somebody to do your \r\n" );
document.write( "\r\n" );
document.write( "homework for you.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );