document.write( "Question 170163: List all Applicable Information for the conic given in standard form. If the information isn't needed for the conic, write N/A. Show Work. (We have to graph it, but i dont think we can graph on this website. I just wanted to check if my graph was right with your answers.)
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Algebra.Com's Answer #125636 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Yes we can graph on here!\r\n" );
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document.write( "We recognize this as an ellipse because the coefficients of\r\n" );
document.write( " and  when on the same side of the\r\n" );
document.write( "equation are both positive and unequal. Also the coefficient \r\n" );
document.write( "of  is smaller than the coefficient of .  \r\n" );
document.write( "So the graph will looks like the number 0 (zero).  That is, \r\n" );
document.write( "its major axis will be vertical.\r\n" );
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document.write( "We must get it in the standard form:\r\n" );
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document.write( "Factor 36 out of the first two terms on the left,\r\n" );
document.write( "and factor 25 out of the last two terms on the\r\n" );
document.write( "left:\r\n" );
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document.write( "Multiply the coefficient of x, which is -8,\r\n" );
document.write( "by , getting .  Then square\r\n" );
document.write( " and get .  Add ,\r\n" );
document.write( "which amounts to adding zero, inside the first\r\n" );
document.write( "parentheses:\r\n" );
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document.write( "Multiply the coefficient of y, which is -6,\r\n" );
document.write( "by , getting .  Then square\r\n" );
document.write( " and get .  Add ,\r\n" );
document.write( "which amounts to adding zero, inside the second\r\n" );
document.write( "parentheses: \r\n" );
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document.write( "Group the first three terms in each parentheses\r\n" );
document.write( "and factor:\r\n" );
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document.write( "Write the factorizations as squares of binomials:\r\n" );
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document.write( "Distribute the 36 and the 25 into the outer\r\n" );
document.write( "sets of parentheses, leaving the squares of\r\n" );
document.write( "binomials intact:\r\n" );
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document.write( "Get a 1 on the right by dividing every term\r\n" );
document.write( "by 900:\r\n" );
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document.write( "Comparing this to the form\r\n" );
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document.write( "We see that \r\n" );
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document.write( "So the center is the point (h,k) = (4,3)\r\n" );
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document.write( "Let's plot the center (4,3):\r\n" );
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document.write( "Now since the ellipse's major axis is vertical, and since a = 6,\r\n" );
document.write( "draw a vertical line from the center extending 6 units upward,\r\n" );
document.write( "which will put it end at the point (4,9).  That will be one of \r\n" );
document.write( "the vertices.\r\n" );
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document.write( "Also draw another vertical line from the center extending 6 units\r\n" );
document.write( "downward, which will put its end at the point (4,-3) which will be\r\n" );
document.write( "the other vertex.\r\n" );
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document.write( "since b = 5, draw a horizontal line from the center extending 5 units to the\r\n" );
document.write( "right, which will put its end at the point (9,3).  That will be one of \r\n" );
document.write( "the covertices.\r\n" );
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document.write( "Also draw a horizontal line from the center extending 5 units to the\r\n" );
document.write( "left, which will put its end at the point (-1,3).  That will be the \r\n" );
document.write( "other covertex:\r\n" );
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document.write( "Now we can sketch in the graph, approximately:\r\n" );
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document.write( "We need to find the foci:\r\n" );
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document.write( "These are located  units from the center on the major \r\n" );
document.write( "axis, where .\r\n" );
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document.write( "So we calculate :\r\n" );
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document.write( "So the foci are the points:\r\n" );
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document.write( "The eccentricity is given by the formula \r\n" );
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document.write( "You may not have studied that ellipses have \r\n" );
document.write( "two directrices. Anyway, for an ellipse elongated\r\n" );
document.write( "vertically the equations of the two directrices\r\n" );
document.write( "of the ellipse is given by the equation\r\n" );
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document.write( "I won't draw these, since they are horizontal lines\r\n" );
document.write( "both off the graph shown.\r\n" );
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document.write( "Center:   \r\n" );
document.write( "Covertices:  \r\n" );
document.write( "Focus or Foci:  \r\n" );
document.write( "Asymptopes:   N/A\r\n" );
document.write( "Major Axis: \r\n" );
document.write( "Transverse Axis:  N/A \r\n" );
document.write( "Directrix: If you've studied directrices of ellipse, they are\r\n" );
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document.write( "Vertices/Vertex:  \r\n" );
document.write( "Radius:  N/A\r\n" );
document.write( "Eccentricity: \r\n" );
document.write( "Minor Axis:   \r\n" );
document.write( "Conjugate Axis:  N/A \r\n" );
document.write( "Axis of Symmetry: There are two axes of symmetry. The horizontal axis of\r\n" );
document.write( "                  symmetry is the line y=3 and the vertical line of \r\n" );
document.write( "                  symmetry is the line x=4.\r\n" );
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document.write( "Edwin

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