document.write( "Question 717075: how can I solve this use the eccentricity of each hyperbola to find its equation in standard form center(4,1),horizontal transverse axis is 12 and eccentricity 4/3 \n" ); document.write( "
Algebra.Com's Answer #440079 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
how can I solve this use the eccentricity of each hyperbola to find its equation in standard form center(4,1),horizontal transverse axis is 12 and eccentricity 4/3.
\n" ); document.write( "
\r\n" );
document.write( "You need to know 5 things about hyperbolas to solve this problem:\r\n" );
document.write( "\r\n" );
document.write( "1. The equation of a hyperbola with horizontal transverse axis is \r\n" );
document.write( "\"%28x-h%29%5E2%2Fa%5E2\"\"%22%22-%22%22\"\"%28y-k%29%5E2%2Fb%5E2\"\"%22%22=%22%22\"\"1\"\r\n" );
document.write( "\r\n" );
document.write( "2. The length of the transverse axis is \"2a\", \r\n" );
document.write( "\r\n" );
document.write( "3. The eccentricity is \"c%2Fa\",\r\n" );
document.write( "\r\n" );
document.write( "4. The center is \"%22%28h%2Ck%29%22\"\r\n" );
document.write( "\r\n" );
document.write( "5. \"c%5E2\"\"%22%22=%22%22\"\"a%5E2%2Bb%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "center(4,1) \r\n" );
document.write( "\r\n" );
document.write( "That tells us that h = 4 and k = 1\r\n" );
document.write( "\r\n" );
document.write( "horizontal transverse axis is 12\r\n" );
document.write( "\r\n" );
document.write( "That tells us that 2a = 12\r\n" );
document.write( "                    a = 6\r\n" );
document.write( "\r\n" );
document.write( "eccentricity 4/3\r\n" );
document.write( "\r\n" );
document.write( "That tells us that   \"c%2Fa+=+4%2F3\"\r\n" );
document.write( "\r\n" );
document.write( "Substituting a = 6,  \"c%2F6+=+4%2F3\"\r\n" );
document.write( "Cross multiplying,   \"3c+=+24\"\r\n" );
document.write( "                     \"+c+=+8\"\r\n" );
document.write( "\r\n" );
document.write( "\"c%5E2\"\"%22%22=%22%22\"\"a%5E2%2Bb%5E2\"\r\n" );
document.write( "\"8%5E2\"\"%22%22=%22%22\"\"6%5E2%2Bb%5E2\"\r\n" );
document.write( "\"64\"\"%22%22=%22%22\"\"36%2Bb%5E2\"\r\n" );
document.write( "\"28\"\"%22%22=%22%22\"\"b%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "So\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-h%29%5E2%2Fa%5E2\"\"%22%22-%22%22\"\"%28y-k%29%5E2%2Fb%5E2\"\"%22%22=%22%22\"\"1\"\r\n" );
document.write( "\r\n" );
document.write( "becomes:\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-4%29%5E2%2F6%5E2\"\"%22%22-%22%22\"\"%28y-1%29%5E2%2F28\"\"%22%22=%22%22\"\"1\"\r\n" );
document.write( "    \r\n" );
document.write( "\"%28x-4%29%5E2%2F36\"\"%22%22-%22%22\"\"%28y-1%29%5E2%2F28\"\"%22%22=%22%22\"\"1\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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