document.write( "Question 1177760: Find an equation of the set of points on a plane such that the sum of the distances between each point of the set and the points (0,3) and (0,-3) is 10 units. \n" ); document.write( "

Algebra.Com's Answer #806891 by ikleyn(52799) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Find an equation of the set of points on a plane such that the sum of the distances
\n" ); document.write( "between each point of the set and the points (0,3) and (0,-3) is 10 units.
\n" ); document.write( "~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "This set of points is the ellipse on a coordinate plane, centered at the origin\r\n" );
document.write( "\r\n" );
document.write( "and having focuses at given points (0,3)  and  (0,-3).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Its major axis is vertical; minor axis is horizontal;\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "the major semi-axis \"a\" has the length \r\n" );
document.write( "\r\n" );
document.write( "    (a-3) + (a-(-3)) =10,  or, equivalently,  (a-3) + (a+3) = 10,  2a = 10,  a = 5 units.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The minor semi-axis \"b\" has the length  b =  =  =  = 4 units.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The canonical equation of this ellipse is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     +  = 1.      ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "On canonical equation for ellipses, see the lesson\r
\n" ); document.write( "\n" ); document.write( " - Ellipse definition, canonical equation, characteristic points and elements \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );