document.write( "Question 1029315: Calculate the eccentricity e of the ellipse. (Enter your answer in exact form.)
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Algebra.Com's Answer #644367 by Edwin McCravy(20059) $\"\"$ $\"About$

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(4, 7) and (4, -3); c = 1
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document.write( "The ellipse looks almost like a circle, but it's a little \r\n" );
document.write( "taller than it is wide.\r\n" );
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document.write( "The two black points are the two given vertices, (4,7) and (4,-3),\r\n" );
document.write( "the green line between the vertices is the major axis, and we can\r\n" );
document.write( "count that it is 10 units long.  The red point (4,2) is the center.\r\n" );
document.write( "It is the midpoint of the major axis.  The value of \"a\", the semi-\r\n" );
document.write( "major axis is one-half of the major axis 10, therefore the answer\r\n" );
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document.write( "That's all you were asked for, but you could have been asked for\r\n" );
document.write( "the foci (or focal points), the co-vertices, and the equation as well.\r\n" );
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document.write( "The equation of any ellipse with a vertical major axis is \r\n" );
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document.write( "where (h,k) is the center, a = the semi-major axis, and\r\n" );
document.write( "b = the semi-minor axis.\r\n" );
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document.write( "The two blue points (4,1) and (4,3) are the foci (or focal points).  \r\n" );
document.write( "They are the points on the green major axis that are c=1 units from \r\n" );
document.write( "the center.\r\n" );
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document.write( "The blue line is the minor axis.  Half its length, called the\r\n" );
document.write( "semi-minor axis is the value of \"b\".  The equation that is true \r\n" );
document.write( "in every ellipse is that .  Substituting c=1 and \r\n" );
document.write( "a=10,  \r\n" );
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document.write( "So the covertices are the endpoints of the minor axis. we get them\r\n" );
document.write( "by adding and subtracting \"b\" to/from the x-coordinate of the \r\n" );
document.write( "center.  They are \r\n" );
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document.write( "So the equation\r\n" );
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document.write( "becomes:\r\n" );
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document.write( "Edwin

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