document.write( "Question 145168: Find the eccentricity of the ellipse given by
\n" ); document.write( "\"16x%5E2%2B25y%5E2=100\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I have tried:
\n" ); document.write( "\"%2816x%5E2%29%2F100+%2B+%2825y%5E2%29%2F100+=+1\" \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "that reduces to:
\n" ); document.write( "\"4x%5E2%2F25+%2B+1y%5E2%2F4+=1\"\r
\n" ); document.write( "\n" ); document.write( "What do I do next? Please explain if you can! Thanks so very much!
\n" ); document.write( "

Algebra.Com's Answer #105850 by Edwin McCravy(20062)\"\" \"About 
You can put this solution on YOUR website!
Find the eccentricity of the ellipse given by
\n" ); document.write( "\"16x%5E2%2B25y%5E2=100\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I have tried:
\n" ); document.write( "\"%2816x%5E2%29%2F100+%2B+%2825y%5E2%29%2F100+=+1\" \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "that reduces to:
\n" ); document.write( "\"4x%5E2%2F25+%2B+1y%5E2%2F4+=1\"\r
\n" ); document.write( "\n" ); document.write( "What do I do next? Please explain if you can! Thanks so very much!
\n" ); document.write( "
\r\n" );
document.write( "Your error is in thinking that you are necessarily reducing the \r\n" );
document.write( "fractions to lowest terms.  Instead think of it as making the \r\n" );
document.write( "numerators 1.  Sometimes it amounts to reducing the fraction\r\n" );
document.write( "but not always.\r\n" );
document.write( "\r\n" );
document.write( "Do it this way instead. Go back to:\r\n" );
document.write( "\r\n" );
document.write( "\"16x%5E2%2F100+%2B+25y%5E2%2F100+=+1\"\r\n" );
document.write( "\r\n" );
document.write( "Get a \"1\" coefficient where the \"16\" is by \r\n" );
document.write( "multiplying top and bottom of the first fraction by\r\n" );
document.write( "\"%281%2F16%29\", and get a \"1\" coefficient where \r\n" );
document.write( "the \"25\" is on the second fraction by multiplying \r\n" );
document.write( "top and bottom by \"%281%2F25%29\", and we have this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now cancel and that leaves just 1 understood on top:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we have\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2+%2F%28100%2F16%29+%2B+y%5E2%2F%28100%2F25%29+=+1\"\r\n" );
document.write( "\r\n" );
document.write( "And we only need to reduce the fractions on the bottom\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2+%2F%2825%2F4%29+%2B+y%5E2%2F4+=+1\"\r\n" );
document.write( "\r\n" );
document.write( "The larger denominator is \"a%5E2\", and since \"25%2F4%3E4\",\r\n" );
document.write( "\r\n" );
document.write( "we compare the above to:\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2%2Fa%5E2+%2B+y%5E2%2Fb%5E2=1\"\r\n" );
document.write( "\r\n" );
document.write( "So \r\n" );
document.write( "\r\n" );
document.write( "\"a%5E2=25%2F4\"            \"b%5E2=4\"\r\n" );
document.write( "\"a=sqrt%2825%2F4%29\"        \"b=2\" \r\n" );
document.write( "\"a=5%2F2\"\r\n" );
document.write( "\r\n" );
document.write( "Eccentricity of an ellipse = \"c%2Fa\" where \"c%5E2=a%5E2-b%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"c%5E2=a%5E2-b%5E2\"\r\n" );
document.write( "\"c%5E2=%285%2F2%29%5E2-2%5E2\"\r\n" );
document.write( "\"c%5E2=25%2F4-4\"\r\n" );
document.write( "\"c%5E2=25%2F4-4%2F1\"\r\n" );
document.write( "\"c%5E2=25%2F4-%284%2A4%29%2F%281%2A4%29\"\r\n" );
document.write( "\"c%5E2=25%2F4-16%2F4\"\r\n" );
document.write( "\"c%5E2=%2825-16%29%2F4\"\r\n" );
document.write( "\"c%5E2=9%2F4\"\r\n" );
document.write( "\"c=sqrt%289%2F4%29\"\r\n" );
document.write( "\"c=3%2F2\"\r\n" );
document.write( "\r\n" );
document.write( "Eccentricity of this elipse = \r\n" );
document.write( "  \r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );