document.write( "Question 1169036: find the equation of the ellipse if the endpoints of minor axis are (1,3) and (1,-1) with a focus at (-1,1). \n" ); document.write( "
Algebra.Com's Answer #851428 by mccravyedwin(407) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "Notice that on the first page this problem reads this way:\r\n" );
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document.write( "Quadratic-relations-and-conic-sections/1169036 (2020-11-05 01:23:06): \r\n" );
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document.write( "See the \" 2020-11-05 01:23:06 \"?  This means that this problem was posted by a \r\n" );
document.write( "student 4 1/2 years ago on November 5, 2020 at 1:23:06 AM.  The student who\r\n" );
document.write( "posted this is no doubt long gone from the class he or she was taking back in\r\n" );
document.write( "2020, and is no longer a student. \r\n" );
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document.write( "Back in 2020 there were still lots of algebra and trig problems being posted.\r\n" );
document.write( "There weren't enough tutors on here, and many problems like this one scrolled\r\n" );
document.write( "off before the tutors got around to solving them because there were so many.\r\n" );
document.write( "    \r\n" );
document.write( "But then the schools learned that kids can take basic statistics with almost no\r\n" );
document.write( "knowledge of second year algebra, no geometry, or trig. First year algebra\r\n" );
document.write( "is enough mathematics for basic statistics, especially now since it's mostly all\r\n" );
document.write( "done on computers.    \r\n" );
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document.write( "So apparently, now most high school students take statistics instead of trig and\r\n" );
document.write( "college algebra.  That's why practically all posts on here nowadays are\r\n" );
document.write( "statistics problems.  \r\n" );
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document.write( "OK, I'll shut up and do this problem posted back in 2020.  The former students\r\n" );
document.write( "getting solutions in their emails to problems they posted back in 2020 are\r\n" );
document.write( "probably having a good laugh!  J\r\n" );
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document.write( "Find the equation of the ellipse if the endpoints of minor axis are (1,3) and\r\n" );
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document.write( "First draw what is given, the minor axis, and plot a focus at (-1,1).\r\n" );
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document.write( "Since the minor axis is vertical, we know that the major axis is horizontal,\r\n" );
document.write( "and the ellipse is like the cross section of an egg sitting on a table, [and\r\n" );
document.write( "not like the number 0, when the minor axis is horizontal and the major axis is\r\n" );
document.write( "vertical.] So the length of the semi-major axis ' a ' goes under the term with\r\n" );
document.write( "x, and the length of the semi-minor axis ' b ' goes under the term with y.  So\r\n" );
document.write( "the form of the equation is\r\n" );
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document.write( "Where the center is the point (h,k).  \r\n" );
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document.write( "Next, we draw the center, which is the midpoint of the minor axis. We can tell\r\n" );
document.write( "the center is the point (1,1).\r\n" );
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document.write( "so we know that the center (h,k) = (1,1).\r\n" );
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document.write( "So we have everything but ' a '. So we can write this much of the equation:\r\n" );
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document.write( "No we calculate ' a '.\r\n" );
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document.write( "The value \" c \" is the distance from the center to a focus. We can tell that the\r\n" );
document.write( "distance from the center (0,0) to a focus (-1,1) is 2 units, so the value of \r\n" );
document.write( "c = 2.  Then we use the Pythagorean fact of all ellipses, which is\r\n" );
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document.write( " where \r\n" );
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document.write( "a is the length of the semi-major axis,\r\n" );
document.write( "b is the length of the semi-minor axis, and\r\n" );
document.write( "c is the distance from the center to a focus.\r\n" );
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document.write( "Since the minor axis that we drew is 4 units long, the semi-minor axis, b, is\r\n" );
document.write( "half that, or b=2.  So we substitute b=2 and c=2 into\r\n" );
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document.write( "So now we know the equation is\r\n" );
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document.write( "or\r\n" );
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document.write( "      <----ANSWER!\r\n" );
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document.write( "But let's finish drawing the ellipse, because you will be asked to do that:\r\n" );
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document.write( " which is about 2.8.\r\n" );
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document.write( "So draw the major axis, which goes from about 2.8 units left of the center,\r\n" );
document.write( "to about 2.8 units right of the center. \r\n" );
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document.write( "Now we can sketch in the ellipse. \r\n" );
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document.write( "And we might as well plot the other focus which is 2 units on the right of the \r\n" );
document.write( "center.\r\n" );
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document.write( "Edwin
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