document.write( "Question 1092965: Find the equation of ellipse with centre (1, 4),vertex at (1,7) and eccentricity e= 2/3. sketch the graph.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #707643 by ikleyn(52803)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "Notice that the center and the vertex lie in one vertical line x = 1.\r\n" );
document.write( "\r\n" );
document.write( "Hence, the major axis is vertical line x = 1 parallel to y-axis.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, the major semi-axis length is the distance from the ellipse center to the vertex, i.e. 7-4 = 3 units.\r\n" );
document.write( "\r\n" );
document.write( "Further, since the eccentricity is \"2%2F3\", the minor semi-axis is  \"%282%2F3%29%2A3\" = 2 units,  and the ellipse is taller than wide.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the equation of the ellipse is \r\n" );
document.write( "\r\n" );
document.write( "\"%28x-1%29%5E2%2F2%5E2\"} + \"%28y-4%29%5E2%2F3%5E2\" = 1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Ellipse \"%28x-1%29%5E2%2F4\" + \"%28y-4%29%5E2%2F9\" = 1\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "See the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Ellipse definition, canonical equation, characteristic points and elements \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "    - Standard equation of an ellipse\r
\n" ); document.write( "\n" ); document.write( "    - Identify elements of an ellipse given by its standard equation\r
\n" ); document.write( "\n" ); document.write( "    - Find the standard equation of an ellipse given by its elements\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic
\n" ); document.write( "\"Conic sections: Ellipses. Definition, major elements and properties. Solved problems\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "============================
\n" ); document.write( "Dear \"students\" !\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Today is a special day.\r
\n" ); document.write( "\n" ); document.write( "Today I solved  16  problems for you and got back  0  (zero,  ZERO)  \"thanks\"  from you.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It is the absolute record !
\n" ); document.write( "    It is just out of limits of my understanding  !
\n" ); document.write( "        I never saw it before  !\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Thank you very much and wish you to think:   WHO ARE YOU . . . \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );