document.write( "Question 1137157: Find an equation of the ellipse that has center (-2,5)
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Algebra.Com's Answer #754993 by ikleyn(52802) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            To solve this problem, the correct logical chain of arguments should be build (and presented) in a right way.\r
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\n" ); document.write( "\n" ); document.write( "            I do not see this correct logical chain in the solution of the other tutor, so I came to present here this logical chain\r
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\n" ); document.write( "\n" ); document.write( "            and the solution as it should be.\r
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document.write( "(1)  Since the center and the vertex have the same y-coordinates  y= 5, it means that the corresponding semi-axis is horizontal \r\n" );
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document.write( "     and has the length of  9 - (-2) = 9 + 2 = 11 units.\r\n" );
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document.write( "     Thus we have horizontal semi-axis of 11 units long.\r\n" );
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document.write( "(2)  Now, the minor semi-axis is   = 5 units long, as it follows from the given part.\r\n" );
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document.write( "     Since this length is different from 11 units, it means that the minor semi-axis is vertical, parallel to y-axis.\r\n" );
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document.write( "     It also means that 11-unit semi-axis is the major-semi-axis.\r\n" );
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document.write( "     \r\n" );
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document.write( "(3)  Now we have the full information, geometrically describing the given ellipse and, hence, we are ready to write the equation\r\n" );
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document.write( "          +  = 1,    or,  equivalently,\r\n" );
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document.write( "          +  = 1.\r\n" );
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document.write( "     It is your final answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Now you have not only right equation, but the full and correct logical chain of arguments which leads to the equation.\r
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