document.write( "Question 76855: write in standard form\r
\n" ); document.write( "\n" ); document.write( "an ellipse with major axis 6 units long and parallel to the x-axis minor axis 4 units long, and center at (8,6) \n" ); document.write( "
Algebra.Com's Answer #55107 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Learn the two ellipse rules:\r\n" );
document.write( "\r\n" );
document.write( "1. An ellipse with major axis parallel to the x-axis has equation\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\" \r\n" );
document.write( "\r\n" );
document.write( "Where (h,k) is the center, \"a\" is one-half the major axis and\r\n" );
document.write( "and \"b\" is one-half the minor axis.  The foci are the points\r\n" );
document.write( "(h+c,k) and (h-c,k) where \"c+=+sqrt%28a%5E2%2Bb%5E2%29\".  You can\r\n" );
document.write( "always tell which is aČ and which is bČ because aČ is ALWAYS\r\n" );
document.write( "larger than bČ.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2. An ellipse with major axis parallel to the y-axis has equation\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1\" \r\n" );
document.write( "\r\n" );
document.write( "Where (h,k) is the center, \"a\" is one-half the major axis and\r\n" );
document.write( "and \"b\" is one-half the minor axis.  The foci are the points\r\n" );
document.write( "(h,k+c) and (h,k-c) where \"c+=+sqrt%28a%5E2%2Bb%5E2%29\".  You can\r\n" );
document.write( "always tell which is aČ and which is bČ because aČ is ALWAYS\r\n" );
document.write( "larger than bČ.\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Your problem is on the first type\r\n" );
document.write( "\r\n" );
document.write( "an ellipse with major axis 6 units long and parallel to the \r\n" );
document.write( "x-axis; minor axis 4 units long; and center at (8,6)\r\n" );
document.write( "\r\n" );
document.write( "a = 1/2 the major axis = (1/2)(6) = 3\r\n" );
document.write( "b = 1/2 the minor axis = (1/2)(4) = 2\r\n" );
document.write( "(h,k) = (8,6)\r\n" );
document.write( "\r\n" );
document.write( "Substitute in\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\"\r\n" );
document.write( "\r\n" );
document.write( "and get\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-8%29%5E2%2F3%5E2%2B%28y-6%29%5E2%2F2%5E2=1\"\r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-8%29%5E2%2F9%2B%28y-6%29%5E2%2F4=1\"\r\n" );
document.write( "\r\n" );
document.write( "The graph is \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );