Algebra.Com's Answer #762780 by ikleyn(52788)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( " In your post, (a) is not an equation at all.\r
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document.write( " (e) is not an equation of an ellipse. It represents the single point (0,0), which is the origin of the coordinate system.\r
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document.write( " Your equation (g) looks suspicious.\r
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document.write( " I will do (c), (d) and (f) for you.\r
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document.write( "In order to understand my solution, you need to be familiar with the basic notions and formulas related to ellipses.\r
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document.write( "It is the NECESSARY condition to understand what is written in my post.\r
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document.write( "You can learn all the necessary introductory knowledge from my lessons\r
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document.write( " - Ellipse definition, canonical equation, characteristic points and elements \r
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document.write( " - General equation of an ellipse\r
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document.write( " - Identify elements of an ellipse given by its general equation\r
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document.write( "in this site.\r
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document.write( "I will assume that you did it.\r
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document.write( "(c)  +  = 1\r\n" );
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document.write( " It is the standard form of an ellipse equation.\r\n" );
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document.write( " Moreover, it is the canonical form of an ellipse equation.\r\n" );
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document.write( " The ellipse, described by this equation, has the center at the point (0,0), which is the origin of the coordinate system.\r\n" );
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document.write( " The major axis of this ellipse is VERTICAL axis \"y\", while the minor axis is HORIZONTAL axis \"x\".\r\n" );
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document.write( " This ellipse IS TALLER than WIDE.\r\n" );
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document.write( " The major semi-axis has the length of  =  units,\r\n" );
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document.write( " while the minor semi-axis has the length of  = 3 units.\r\n" );
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document.write( " Therefore, the major axis has the length of  units, while the minor axis has the length of 6 units.\r\n" );
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document.write( "(d)  +  = 32.\r\n" );
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document.write( " Divide both sides of this equation by 32. You will get an equivalent equation\r\n" );
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document.write( "  +  = 1.\r\n" );
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document.write( " It is the standard form of an ellipse equation.\r\n" );
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document.write( " Moreover, it is the canonical form of an ellipse equation.\r\n" );
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document.write( " The ellipse, described by this equation, has the center at the point (0,0), which is the origin of the coordinate system.\r\n" );
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document.write( " The major axis of this ellipse is horizontal x-axis, while the minor axis is vertical y-axis.\r\n" );
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document.write( " The major semi-axis has the length of  =  units,\r\n" );
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document.write( " while the minor semi-axis has the length of  = 2 units.\r\n" );
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document.write( " Therefore, the major axis has the length of  units, while the minor axis has the length of 4 units.\r\n" );
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document.write( "(f)  +  = 1. <<<---=== Notice that your original equation was written INCORRECTLY, and I fixed it (!)\r\n" );
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document.write( " Your equation is\r\n" );
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document.write( "  +  = 1.\r\n" );
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document.write( " It is the standard form of an ellipse equation.\r\n" );
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document.write( " ( But not its canonical form ).\r\n" );
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document.write( " The ellipse, described by this equation, has the center at the point (5,-11) of the coordinate system.\r\n" );
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document.write( " The major axis of this ellipse is VERTICAL line parallel to y-axis, while the minor axis is the HORIZONTAL line parallel to x-axis.\r\n" );
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document.write( " This ellipse IS TALLER than WIDE.\r\n" );
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document.write( " The major semi-axis has the length of 12 units,\r\n" );
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document.write( " while the minor semi-axis has the length of 11 units.\r\n" );
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document.write( " Therefore, the major axis has the length of 24 units, while the minor axis has the length of 22 units.\r\n" );
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document.write( "One advise for the future.\r
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document.write( "The rules of this forum require that every post goes with one problem.\r
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document.write( "Do not place many problem in your post - do not violate this rule.\r
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document.write( "When you complete reading my post, do not forget to post your \"THANKS\" back to me.\r
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